Exhibit 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of OncoMed Pharmaceuticals, Inc. (the “Company”) on Form 10-Q for the fiscal quarter ended June 30, 2013, as filed with the Securities and Exchange Commission (the “Report”), Paul J. Hastings, President and Chief Executive Officer of the Company, and William D. Waddill, Senior Vice President and Chief Financial Officer of the Company, respectively, do each hereby certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

• The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

• The information in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: September 3, 2013

/s/ Paul J. Hastings

Paul J. Hastings

President and Chief Executive Officer

(principal executive officer)

/s/ William D. Waddill

William D. Waddill

Senior Vice President and Chief Financial Officer

(principal financial and accounting officer)