Exhibit 99.1

Epizyme Announces Updates to Its Board of Directors

CAMBRIDGE, Mass., November 18, 2021 – Epizyme, Inc. (Nasdaq: EPZM), a fully integrated, commercial-stage biopharmaceutical companydeveloping and delivering novel epigenetic therapies, today announced two appointments to the Company’s Board of Directors: clinical oncology executive, Roy A. Beveridge, M.D., and international pharmaceutical and financial executive, CarolStuckley, M.B.A. The Company today also announced that Andrew R. Allen, M.D., Ph.D., who has served on the Company’s Board of Directors since June 2014, has resigned from this position, also effective November 16, 2021.

“We are delighted to welcome Roy and Carol to our Board of Directors as we broaden our portfolio and solidify our leadership in epigenetictherapies,” said Grant Bogle, President and Chief Executive Officer of Epizyme. “Roy’s broad experience as a practicing clinical oncologist and researcher, coupled with his executive leadership roles as Chief Medical Officer for bothHumana Inc. and US Oncology, Inc., brings crucial payer and provider insights to Epizyme as we deepen our focus on supporting physicians in delivering optimal care to the patients and communities they serve. Carol’s 25+ years of executiveleadership in the healthcare industry, including more than 22 years at Pfizer, coupled with her multinational finance and accounting expertise, make her an ideal director to serve on the Epizyme Board as our commercial activities accelerate. We alsowant to recognize and thank Andrew for his many contributions over his years of service, helping us transition Epizyme to a fully integrated biopharmaceutical company during his seven years on our Board.”

Roy A. Beveridge, M.D., is a medical oncologist who has been in practice for more than 30 years during which time he has treated hundreds of lymphoma andmyeloma patients. He has led large integrated provider networks and has deep expertise in healthcare policy and reimbursement. Previously, Dr. Beveridge served as Humana Inc.’s Chief Medical Officer, where he led clinical policy,population health and clinical quality initiatives. Prior to this Dr. Beveridge held a similar role for US Oncology, which was acquired by McKesson Specialty Health, where he focused on research, quality, data science, clinical pathways andpayer initiatives. Much of his recent work has focused on social determinants of health and improving the health of underserved populations. He has published more than 200 papers in various professional and scientific journals. Dr. Beveridge iscurrently a Strategy and Policy Consultant at Avalere Health, a healthcare consulting firm, and his additional professional experiences include working as a Consultant to Humana and serving as Interim President of Conviva Physician Group, awholly-owned subsidiary of Humana. Dr. Beveridge holds a B.A. in Biology from the Johns Hopkins University and an M.D. from Cornell University. He also received internal medicine training at the University of Chicago and completed an oncologyfellowship at Johns Hopkins University.

Carol Stuckley, M.B.A., is a finance executive with significant experience leading the financial aspects of largeglobal healthcare companies. Ms. Stuckley spent more than 22 years at Pfizer, Inc. in a variety of global financial roles of increasing responsibility, most recently as Vice President, Assistant Treasurer, and Corporate Officer. Shecurrently serves on the Board of Directors of

Centessa Pharmaceuticals plc, a publicly traded clinical-stage pharmaceutical company, and previously served on the Board of Directors of Ipsen S.A., a publicly traded, French pharmaceuticalcompany. Ms. Stuckley recently served as the Chief Financial Officer and Senior Vice President at Healthcare Payment Specialists, LLC (acquired by TransUnion), and as Vice President, Finance North America at Galderma Laboratories, L.P.(acquired by Nestle Skin Health). Ms. Stuckley earned a B.A. in Economics and French from the University of Delaware, as well as an M.B.A. in International Business and Finance and an M.A. in Economics from the Fox Business School at TempleUniversity.

“As Epizyme launches into its next phase of growth, the addition of Roy and Carol and their distinguished and complementary skillsetswill help us further strengthen and diversify our Board,” said David M. Mott, Chairman of the Board of Directors of Epizyme. “I look forward to working alongside them as Epizyme seeks to fulfill its vision of developing transformativeepigenetic medicines for people living with cancer. I would also like to thank Andrew for his dedication and commitment to Epizyme over the last seven years. His input and guidance to the Company have been invaluable, and we wish him well.”

About Epizyme, Inc.

Epizyme, Inc. is a fullyintegrated, commercial-stage biopharmaceutical company committed to its mission of rewriting treatment for cancer through novel epigenetic medicines. The Company is focused on creating medicines that are targeted at specific causes of diseases, thatare orally administered, tolerable, easy to take and based on a deep understanding of the patients that may benefit from them. The Company aspires to change thestandard-of-care for patients and physicians by developing medicines with fundamentally new mechanisms of action. For more information, visit www.epizyme.com.

Media:

Erin Graves

Epizyme, Inc

media@epizyme.com

(617) 500-0615

Investors:

Bill Slattery, Jr.

wslattery@realchemistry.com

Source: Epizyme, Inc.

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