Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We hereby consent to the incorporation by reference in the Registration Statements on Form S-3 (Nos. 333-219834 and 333-228328) and Form S-8 (Nos. 333-210216, 333-196900, 333-204931, 333-216602, 333-22356, 333-228326, 333-230291, and 333-234579) of Zafgen, Inc. of our report dated March 5, 2020 relating to the financial statements, which appears in this Form 10-K.

/s/ PricewaterhouseCoopers LLP

Boston, Massachusetts

March 5, 2020