Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in Registration Statement Nos. 333-125926, 333-137746 and 333-141807 on Form S-3 and 33-23053, 33-38030, 33-65192, 333-38865, 333-66029, 333-103245, 333-114066, 333-123675, 333-123676 and 333-132054 on Form S-8 of our reports dated June 13, 2008, relating to the consolidated financial statements and financial statement schedule of ABIOMED, Inc. (which report expresses an unqualified opinion and includes explanatory paragraphs relating to the adoption of FASB Interpretation No. 48, Accounting for Uncertainty in Income Taxes—an Interpretation of Financial Accounting Standards Board Statement No. 109, as discussed in Note 14 and the adoption of Financial Accounting Standards Board Statement No. 123R, Share-Based Payment, as discussed in Note 2), 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, 2008.

/s/ Deloitte & Touche LLP

Boston, Massachusetts

June 13, 2008