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-1 of Zafgen, Inc., filed pursuant to Rule 462(b) of the Securities Act of 1933, 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 Amendment No. 4 to the Registration Statement on Form S-1 (No. 333-195391). We also consent to the reference to us under the heading “Experts” in Amendment No. 4 to the Registration Statement filed on Form S-1 as incorporated by reference in this Registration Statement.

/s/ PricewaterhouseCoopers LLP

Boston, Massachusetts

June 18, 2014