Exhibit 32.1

Certification by the Chief Executive Officer Pursuant to 18 U.S.C. Section 1350, as Adopted

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

I, George S. Barrett, Chairman and Chief Executive Officer of Cardinal Health, Inc. (the “Company”), certify, pursuant to 18 U.S.C. Section 1350, that:

(1) the Quarterly Report on Form 10-Q for the quarter ended March 31, 2012 containing the financial statements of the Company (the “Periodic Report”), which this statement accompanies, fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 (15 U.S.C. 78m or 78o(d)); and

(2) the information contained in the Periodic Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: May 8, 2012

/s/ George S. Barrett

George S. Barrett

Chairman and Chief Executive Officer