Crafting Highly Selective Kinase Medicines for Patients With Genomically Defined Diseases January 11, 2016 Exhibit 99.1

This presentation contains forward-looking statements as defined in the Private Securities Litigation Reform Act of 1995, as amended. The words “may,” “will,” “could,” “would,” “should,” “expect,” “plan,” “anticipate,” “intend,” “believe,” “estimate,” “predict,” “project,” “potential,” “continue,” “target” and similar expressions are intended to identify forward-looking statements, although not all forward-looking statements contain these identifying words. In this presentation, forward-looking statements include, without limitation, statements about plans and timelines for the clinical development of BLU-554 and BLU-285; the potential benefits of BLU-554 in treating patients with hepatocellular carcinoma; the potential benefits of BLU-285 in treating patients with gastrointestinal stromal tumors and systemic mastocytosis; the potential of RET and NTRK fusions and their predicted resistant mutants as therapeutic targets; the potential of PRKACA fusions as therapeutic targets; the potential of kinases as therapeutic targets in tumor immunity; the timing of clinical data or proof of concept for preclinical and clinical programs; the timing of regulatory submissions or filings, including, without limitation, an investigational new drug application for BLU-667; plans and timelines for the development of companion diagnostics for BLU-554 and BLU-285; plans and timelines for additional discovery programs; the future financial performance of Blueprint Medicines Corporation (the “Company”); and the Company’s strategy, business plans and focus. The Company has based these forward-looking statements on management’s current expectations, assumptions, estimates and projections. While the Company believes these expectations, assumptions, estimates and projections are reasonable, such forward-looking statements are only predictions and involve known and unknown risks, uncertainties and other important factors, many of which are beyond the Company’s control and may cause actual results, performance or achievements to differ materially from those expressed or implied by any forward-looking statements. These risks and uncertainties include, without limitation, risks and uncertainties related to the delay of any current or planned clinical trials or the development of the Company’s drug product candidates, including BLU-285 and BLU-554; the Company’s ability to successfully demonstrate the efficacy and safety of its drug product candidates; the preclinical and clinical results for the Company’s drug product candidates, which may not support further development of such drug product candidates; the content and timing of decisions made by the U.S. Food and Drug Administration and other regulatory authorities, investigational review boards at clinical trial sites and publication review bodies, which may affect the initiation, timing and progress of clinical trials; the Company’s ability to obtain and maintain requisite regulatory approvals and to enroll patients in its planned clinical trials; the Company’s ability to obtain, maintain and enforce patent and other intellectual property protection for any product candidates it is developing; and the Company’s ability to maintain key collaborations, such as its agreement with Alexion Pharma Holding. These and other risks and uncertainties are described in greater detail under “Risk Factors” in the Company’s Quarterly Report on Form 10-Q for the quarter ended September 30, 2015, as filed with the Securities and Exchange Commission (“SEC”) on November 9, 2015, and any other filings the Company may make with the SEC in the future. The Company cannot guarantee future results, outcomes, levels of activity, performance, developments, or achievements, and there can be no assurance that the Company’s expectations, intentions, anticipations, beliefs, or projections will result or be achieved or accomplished. The forward-looking statements in this presentation are made only as of the date hereof, and except as required by law, the Company undertakes no obligation to update any forward-looking statements contained in this presentation as a result of new information, future events or otherwise. This presentation also contains estimates, projections and other statistical data made by independent parties and by the Company relating to market size and growth and other data about the Company’s industry. These data involve a number of assumptions and limitations, and you are cautioned not to give undue weight to such estimates. In addition, projections, assumptions and estimates of the Company’s future performance and the future performance of the markets in which the Company operates are necessarily subject to a high degree of uncertainty and risk. Forward-Looking Statements

Crafting Highly Selective Kinase Medicines for Patients With Genomically Defined Diseases >$17bn in small molecule kinase drug sales in 2014 Continued platform potential to generate new programs in 2016 and beyond Initial data potential by end of 2016 from 3 Phase 1 trials IND filing for BLU-667 (RET fusions / resistant mutants) anticipated by end of 2016 Nomination of additional discovery programs with rapid development potential through enriched clinical trials Three Phase I trials BLU-285 for gastrointestinal stromal tumor (GIST): Phase 1 enrolling BLU-285 for advanced systemic mastocytosis (SM): IND accepted, clinical sites opening BLU-554 for hepatocellular carcinoma (HCC): Phase 1 enrolling Novel Selective Kinase Platform Two Lead Programs: 3 Clinical Trials Near-Term Milestones Large Opportunity Highly Experienced Team Systematic, reproducible approach to identify kinase drivers of disease and craft drug candidates Integrated new target discovery engine and proprietary compound library Demonstrated productivity including Alexion collaboration Deep expertise in oncology and rare genetic diseases Successful track records in discovery and development of drugs to genomic drivers of disease

Poised to Build a Fully Integrated Business Potential for rapid clinical path in defined patient groups Multiple wholly-owned assets enabling a staged approach to potential commercialization in as little as 5 years Blueprint Medicines is Positioned to Build a Sustainable Business Prolific Discovery Engine 1 IND per year on average 6 programs; plan to nominate 2 more in 2016 Expertise to mine potential of Kinases of Unknown Biology Strategic collaboration opportunities Clinical Stage Pipeline 2016 expected milestones: BLU-285 POC in GIST BLU-285 POC in SM BLU-554 POC in HCC Develop CDx’s for patient selection BLU-667 RET IND filing Strong financial position with cash through at least early 2017 Untapped kinase opportunity in oncology, rare genetic diseases and beyond Focused on kinase-driven diseases with high medical need Potential for transformative impact in genomically defined patient populations

Led by a Team of Industry Innovators With Deep Expertise and Track Records of Success Christoph Lengauer, Ph.D. Chief Scientific Officer Jeff Albers Chief Executive Officer and President Andy Boral, M.D., Ph.D. Chief Medical Officer Prior Experience: Executive Management Raised $169M Gross in 2015 IPO (NASDAQ: BPMC) Kate Haviland Chief Business Officer

Platform Integrates Innovative Target Discovery Engine and Proprietary Compound Library to Yield Novel Drug Candidates Novel chemical matter Broad, diverse kinome coverage Annotated for rapid prosecution of medicinal chemistry Precisely tailored target product profiles Compound Library Proprietary genomic analyses algorithms Precision functional genomics Specific emphasis on kinases of unknown biology (KUBs) Proven expertise in predicting drug resistance Target Discovery Engine Novel kinase targets of disease Highly selective kinase medicines Unique chemistry for difficult to drug targets Kinome illustration reproduced courtesy of CSTI (www.cellsignal.com). The foregoing website is maintained by CSTI, and Blueprint Medicines is not responsible for its content.

Initial Indications Stage of Development Commercial Rights BLU-285 (KIT Exon 17 Mutants and PDGFRα D842V Inhibitor) GIST Phase 1 Enrolling SM IND Accepted BLU-554 (FGFR4 Inhibitor) HCC Phase 1 Enrolling BLU-667 (RET Fusions & Resistant Mutants) NSCLC, thyroid Pre-clinical Rare Genetic Disease Target Rare genetic disease Undisclosed Diverse Portfolio With Clinical Stage Assets Ongoing discovery: NTRK fusions / resistant mutants & undisclosed 6th program Platform Potential: 1 IND per Year on Average

BLU-285 is a Selective and Potent Inhibitor of Exon 17 Mutant KIT and D842V Mutant PDGFRα in GIST Models Gastrointestinal Stromal Tumor Advanced GIST Details Patients* PDGFRα D842V 5-6% 500 Relapsed/ Refractory GIST 2L and beyond 12,000 1L GIST 1L 8,000 *GIST patient estimates represent incidence in US, EU5 and Japan. Sarcoma of the digestive tract Overall survival of ~5 years Imatinib and other kinase inhibitors do not provide a cure, as resistance mutations in KIT Exon 17 ultimately arise No therapy addresses PDGFRα D842 mutations Patient-Derived Treatment-Resistant GIST Xenograft

BLU-285 is a Selective and Potent Inhibitor of D816V Mutant KIT in SM Models Systemic Mastocytosis SM Subtypes Disease Burden Patients* Advanced SM >94% with KIT D816V mutation 4,500 Indolent SM 16,000 *SM patient estimates represent prevalence in these markets. Mast cell disorder Patients experience severe allergy symptoms Advanced SM patients suffer from organ dysfunction due to mast cell infiltration – overall survival of 3 – 5 years No therapy addresses the underlying disease biology Mouse Mastocytoma Allograft Model Vehicle BLU-285, 0.3 mg/kg/d BLU-285, 1 mg/kg/d BLU-285, 3 mg/kg/d Dasatinib 25 mg/kg bid BLU-285, 10 mg/kg/d BLU-285, 30 mg/kg/d Study Days Tumor Volume (mm3)

BLU-285: Two Phase 1 Clinical Studies Underway SM Expansion SM Dose Escalation Three groups of patients Aggressive SM Aggressive SM with another hematologic disorder Mast cell leukemia ~35 patients 2015 2017 GIST Expansion GIST Dose Escalation Two groups of patients KIT Exon 17 mutations PDGFRα D842V mutation ~35 patients Potential for POC by end of 2016 SM Key Endpoints Primary Safety MTD Secondary Response rate Serum tryptase Allele burden Symptoms GIST Key Endpoints Primary Safety MTD Secondary Response rate Pharmacokinetics Allele burden 3+3 design: ~25 patients Starting dose: 30 mg / day Retrospective KIT D816V testing 3+3 design: ~25 patients Starting dose: 30 mg / day Retrospective KIT Exon 17 and PDGFRα testing Enrolling Sites opening 2016 2015 2017 2016

Hepatocellular Carcinoma Advanced HCC Subsets Patients* 1L with FGFR4 activation 18,000 2L with FGFR4 activation 6,000 Liver cancer, most often HCC, is 2nd leading cause of cancer death worldwide Sorafenib only approved drug, no approved 2nd line therapy Up to 30% of HCC patients have abnormally active FGFR4 pathway, a validated driver No genomically targeted therapies available *Represents prevalence in key markets including US, EU5 and Japan BLU-554 Activity in Xenograft Model With Amplified FGF19 BLU-554 is a Selective and Potent Inhibitor of FGFR4 in HCC models

Key Endpoints Primary Safety MTD Secondary Response rate Pharmacokinetics Alpha fetoprotein FGF19 in blood CYP7A1 RNA in tumor Patients selected for FGF19 expression by IHC ~25 HCC patients ~10 cholangiocarcinoma patients Expansion HCC Dose Escalation 3+3 design: ~25 patients Starting dose: 140 mg / day Retrospective FGF19 expression and amplification testing 2015 2017 Potential for POC by end of 2016 2016 BLU-554: Phase 1 Clinical Study Underway Enrolling

Robust activity against wild-type RET as well as known and predicted resistance mutations Tumor regression in animal models driven by RET fusion proteins Initiate 28-day GLP toxicology 1H 2016 with IND filing anticipated by end of 2016 Approach Differentiated from Multi-kinase Inhibitors With RET Activity RET Initial Indications Disease Frequency* Patients** Lung Adenocarcinoma 1-2% 2,500 Medullary Thyroid Cancer 60% 400 Papillary Thyroid Cancer 10% 500 *Represents estimated frequency of RET fusion for Lung and PTC and estimated frequency of activating point mutations for MTC. **Represents estimated incidence in US, EU5 and Japan. BLU-667 is a Selective and Potent Inhibitor of RET in Non-Clinical Development for RET-driven Tumors

RET Program: Potent In Vivo Activity in RET and Predicted Resistance Mutants Vehicle 20mpk Reference QD 10mpk BLU6864 QD 30mpk BLU6864 QD 60mpk BLU6864 QD Ref BLU6864 Activity of BLU6864 (tool compound) in RET Fusion Allograft BLU6864 Ref Vehicle 20mpk Reference QD 10mpk BLU6864 QD 30mpk BLU6864 QD 60mpk BLU6864 QD Activity of BLU6864 (tool compound) in RET V804L Mutant Fusion Allograft

Alexion Collaboration Leverages Blueprint Platform in Rare Genetic Diseases Collaboration Highlights Objective is to develop the first kinase inhibitor specifically designed for a rare and devastating genetic disease Blueprint Medicines is responsible for: Identification & optimization of drug candidates Biomarker discovery All pre-IND activities Alexion is responsible for: Clinical development Commercialization >$250M in potential milestones Kinase-Focused Drug Discovery Rare Genetic Disease Expertise

Immunokinase Opportunity Activation Tumor immunity (Replace or add on to checkpoint inhibitors) Inhibition Autoimmunity (MS, Lupus, RA) J Clin Invest. (2015) 125:1780-9. Kinases are critically involved in all aspects of immune system signaling

Clinical Development BLU-285 GIST IND accepted; Phase I trial enrolling patients in dose escalation BLU-285 SM IND accepted; Phase 1 clinical sites opening BLU-554 HCC IND accepted; Phase I trial enrolling patients in dose escalation Received orphan drug designation for BLU-554 in HCC Discovery Selected development candidates for RET and NTRK Initiated undisclosed 6th discovery program Presented at five major medical conferences and published two peer-reviewed publications Corporate Raised $169M gross in upsized IPO Announced collaboration with Alexion for rare genetic disease program Received $15M upfront payment and achieved first preclinical milestones Continued to attract top discovery, clinical and business talent Blueprint Medicines Achieved 2015 Goals

Financial Overview* Market Cap ~$580M Shares Outstanding - Basic - Fully Diluted 27.1M 29.1M Outstanding Debt $7.9M Cash Position $179.8M Blueprint Medicines (BPMC): Entering 2016 in a Position of Financial Strength Ownership Summary* Existing cash balance expected to be sufficient to fund operations and capital expenditures through at least early 2017 *As of 9/30/2015, with the exception of the Market Cap, which is as of 1/6/2016 71% 21% 5% 3% Top 10 holders Other Institutional Retail/Other Insider

Clinical Development Report preliminary data from three ongoing trials BLU-285 in GIST BLU-285 in SM BLU-554 in HCC Finalize companion diagnostic development for BLU-285 and BLU-554 programs Discovery Advance RET BLU-667 to IND filing Disclose 6th discovery program Internally nominate 2 new discovery programs including at least one in immuno-oncology Corporate Maintain financial strength with cash for clinical proof of concept for three lead programs Continue to explore strategic collaborations that allow us to maximize the value of our platform 2016 Goals: Advance 3 Trials to Clinical POC While Continuing to Progress Diversified Discovery Portfolio