Exhibit 32.1

CERTIFICATION OF CHIEF EXECUTIVE OFFICER AND CHIEF FINANCIAL OFFICER

PURSUANT TO RULE 13a-14(b) UNDER THE SECURITIES EXCHANGE ACT OF 1934 AND 18 U.S.C. SECTION 1350

AS ADOPTED PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with this quarterly report on Form 10-Q of Medical Properties Trust, Inc. (the “Company”) for the quarter ended March 31, 2024 (the “Report”), each of the undersigned, Edward K. Aldag, Jr. and R. Steven Hamner, certifies, pursuant to Section 18 U.S.C. Section 1350, that:

1.The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

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

Date: May 29, 2024	/s/ Edward K. Aldag, Jr.
	Edward K. Aldag, Jr.
	Chairman, President and Chief Executive Officer
	/s/ R. Steven Hamner
	R. Steven Hamner
	Executive Vice President and Chief Financial Officer