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 Registration Statement Nos. 33-23053, 33-38030, 33-65192, 333-38865, 333-66029, 333-103245, 333-114066, 333-123675, 333-123676, 333-132054, 333-152989, 333-176620 and 333-186613 on Form S-8 of our reports dated May 28, 2014, 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, appearing in this Annual Report on Form 10-K of ABIOMED, Inc. and subsidiaries, for the year ended March 31, 2014.

/s/ Deloitte & Touche LLP

Boston, Massachusetts

May 28, 2014