Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the reference to our firm under the caption “Experts” in the Registration Statement (Form S-3) and related Prospectus of Five Prime Therapeutics, Inc. for the registration of up to $250,000,000 of common stock and to the incorporation by reference therein of our report dated February 27, 2018 with respect to the financial statements of Five Prime Therapeutics included in its Annual Report (Form 10-K) for the year ended December 31, 2017, filed with the Securities and Exchange Commission.

/s/ Ernst & Young LLP

San Francisco, California

November 6, 2018