Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the Registration Statement (Form S-8 No. 333-191700) pertaining to the 2002 Equity Incentive Plan, the 2010 Equity Incentive Plan, the 2013 Omnibus Incentive Plan, and the 2013 Employee Stock Purchase Plan of Five Prime Therapeutics Inc. of our report dated March 25, 2014, with respect to the financial statements Five Prime Therapeutics, Inc. included in its Annual Report (Form 10-K) for the year ended December 31, 2013, filed with the Securities and Exchange Commission.

/s/ Ernst & Young LLP

Redwood City, California

March 25, 2014