QuickLinks -- Click here to rapidly navigate through this document

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 Annual Report of Acceleron Pharma Inc. (the "Company") on Form 10-K for the period ending December 31, 2013 as filed with the Securities and Exchange Commission on the date hereof (the "Report"), I, John Knopf, as the Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. 1350, as adopted pursuant to section 906 of the Sarbanes-Oxley Act of 2002, that, to the best of my knowledge:

(1)

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



(2)

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

Date: March 17, 2014

/s/ JOHN L. KNOPF
John L. Knopf*
Chief Executive Officer

*

A signed original of this written statement required by Section 906 has been provided to Acceleron Pharma Inc. and will be retained by Acceleron Pharma Inc. and furnished to the Securities and Exchange Commission or its staff upon request.

        The foregoing certification is being furnished solely pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United States Code) and is not being filed as part of the Form 10-K or as a separate disclosure document.

QuickLinks

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