Exhibit 32.1

CERTIFICATE PURSUANT TO 18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

I, Stephen J. Hagge, president and chief executive officer of AptarGroup, Inc., certify that (i) the Quarterly Report on Form 10-Q of AptarGroup, Inc. for the quarter ended March 31, 2016 (the “Form 10-Q”) fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934 and (ii) the information contained in the Form 10-Q fairly presents, in all material respects, the financial condition and results of operations of AptarGroup, Inc.

/s/ STEPHEN J. HAGGE

Stephen J. Hagge

President and Chief Executive Officer

May 3, 2016