Exhibit 32.1

CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350

COVIDIEN PLC

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

The undersigned officers of Covidien plc (the “Company”) hereby certify to their knowledge that the Company’s annual report on Form 10-K for the period ended September 27, 2013 (the “Report”), as filed with the Securities and Exchange Commission on the date hereof, fully complies with the requirements of Section 13(a) or 15(d), as applicable, of the Securities Exchange Act of 1934, as amended, and that the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/    José E. Almeida

José E. Almeida

Chairman, President and Chief Executive Officer

November 21, 2013

/s/    Charles J. Dockendorff

Charles J. Dockendorff

Executive Vice President and Chief Financial Officer

November 21, 2013