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 and 333-152755 on Form S-3 and 33-23053, 33-38030, 33-65192, 333-38865, 333-66029, 333-103245, 333-114066, 333-123675, 333-123676, 333-132054 and 333-152989 on Form S-8 of our reports dated June 8, 2009, relating to the consolidated financial statements and financial statement schedule of ABIOMED, Inc. (which report expresses an unqualified opinion and includes an explanatory paragraph relating to the adoption of Financial Accounting Standards Board (FASB) Interpretation No. 48, Accounting for Uncertainty in Income Taxes an Interpretation of Financial Accounting Standards Board Statement No. 109), and the effectiveness of ABIOMED, Inc.’s internal control over financial reporting, appearing in this Annual Report on Form 10-K of ABIOMED, Inc. for the year ended March 31, 2009.

/s/ Deloitte & Touche LLP

Boston, Massachusetts

June 8, 2009