Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We hereby consent to the incorporation by reference in this Registration Statement on Form S-8 of our report dated March 24, 2015 relating to the financial statements, which appears in Zafgen, Inc.‘s Annual Report on Form 10-K for the year ended December 31, 2014.

/s/ PricewaterhouseCoopers LLP

Boston, Massachusetts

June 12, 2015