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 of ABIOMED, Inc. and subsidiaries (which report expresses an unqualified opinion and includes an explanatory paragraph relating to the Company’s adoption of Accounting Standards Update No. 2016-09, Compensation – Stock Compensation: Improvements to Employee Share-Based Payment Accounting), and the effectiveness of ABIOMED, Inc.’s and subsidiaries internal control over financial reporting dated May 24, 2018, appearing in the Annual Report on Form 10-K of ABIOMED, Inc. for the year ended March 31, 2018.

/s/ DELOITTE & TOUCHE LLP

Boston, Massachusetts

September 7, 2018