Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in Registration Statement Nos. 333-38865, 333-66029, 333-103245, 333-114066, 333-123675, 333-123676, 333-132054, 333-152989, 333-176620, 333-186613, 333-206395, 333-209414 and 333-213319 on Form S-8 of our reports dated May 25, 2017, relating to the consolidated financial statements 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. for the year ended March 31, 2017.

/s/ DELOITTE & TOUCHE LLP

Boston, Massachusetts

May 25, 2017