Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the Registration Statement (Form S-8) pertaining to the 2013 Omnibus Incentive Plan and the 2013 Employee Stock Purchase Plan of Five Prime Therapeutics, Inc. of our reports dated February 26, 2019, with respect to the financial statements of Five Prime Therapeutics, Inc. and the effectiveness of internal control over financial reporting of Five Prime Therapeutics, Inc. included in its Annual Report on Form 10-K for the year ended December 31, 2018, filed with the Securities and Exchange Commission.

/s/ Ernst & Young LLP

San Francisco, California

May 9, 2019