Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in this Registration Statement on Form S-8 of our reports dated June 4, 2012, relating to the financial statements and financial statement schedule of ABIOMED, Inc., and the effectiveness of ABIOMED, Inc.’s internal control over financial reporting, appearing in the Annual Report on Form 10-K of ABIOMED, Inc. for the year ended March 31, 2012.

/s/ Deloitte & Touche LLP

Boston, Massachusetts

February 12, 2013