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 relating to the consolidated financial statements and financial statement schedule of ABIOMED, Inc. and subsidiaries and the effectiveness of ABIOMED, Inc.’s and subsidiaries internal control over financial reporting dated May 28, 2015, appearing in the Annual Report on Form 10-K of ABIOMED, Inc. for the year ended March 31, 2015.

/s/ DELOITTE & TOUCHE LLP

Boston, Massachusetts

February 5, 2016