Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in Registration Statement Nos. 333-125926, 333-141807, 333-152755 and 333-159886 on Form S-3 and 33-23053, 33-38030, 33-65192, 333-38865, 333-66029, 333-103245, 333-114066, 333-123675, 333-123676, 333-132054, 333-152989 and 333-176620 on Form S-8 of our reports dated June 4, 2012, relating to the consolidated financial statements and financial statement schedule of ABIOMED, Inc., and the effectiveness of ABIOMED, Inc.’s internal control over financial reporting, appearing in this Annual Report on Form 10-K of ABIOMED, Inc. for the year ended March 31, 2012.

/s/ Deloitte & Touche LLP

Boston, Massachusetts

June 4, 2012