EXHIBIT 23.1

Consent of Independent Registered Public Accounting Firm

The Board of Directors

Cyberonics, Inc.:

We consent to the incorporation by reference in the registration statements (Nos. 333-185500, 333-163219, 333-143821, 333-125401, 333-108281, 333-102521, 333-97095, 333-56694 and 333-66691) on Forms S-8 of Cyberonics, Inc. of our reports dated June 19, 2013, with respect to the consolidated balance sheets of Cyberonics, Inc. as of April 26, 2013 and April 27, 2012, and the related consolidated statements of income, comprehensive income, stockholders’ equity and cash flows for the 52 weeks ended April 26, 2013, April 27, 2012 and April 29, 2011, and the effectiveness of internal control over financial reporting as of April 26, 2013, which reports appear in the April 26, 2013 annual report on Form 10-K of Cyberonics, Inc.

/s/ KPMG LLP  

Houston, Texas

June 19, 2013