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 14, 2014, except for Note 17, as to which the date is June 5, 2014, relating to the consolidated financial statements of Zafgen, Inc., which appears in Zafgen, Inc.’s Amendment No. 4 to the Registration Statement on Form S-1 (No. 333-195391).

/s/ PricewaterhouseCoopers LLP

Boston, Massachusetts

June 18, 2014