UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON D.C. 20549

FORM 6-K

REPORT OF FOREIGN PRIVATE ISSUER

PURSUANT TO RULE 13a-16 OR 15d-16

OF THE SECURITIES EXCHANGE ACT OF 1934

April 2026

Commission File Number: 001-43208

The Metals Royalty Company Inc.

1900 Dome Tower

333 7^th Ave SW

Calgary, AB, T2P 2Z1

British Columbia, Canada

(403) 984-1941

(Address of principal executive offices)

Indicate by check mark whether the registrant files or will file annual reports under cover Form 20-F or Form 40-F.

Form 20-F   x Form 40-F   ¨

INFORMATION CONTAINED IN THIS REPORT ON FORM 6-K

On April 1, 2026, The Metals Royalty Company Inc (the “Company”). announced that its registration statement on Form F-1 (the “Registration Statement”) has been declared effective by the U.S. Securities and Exchange Commission and that the Company’s common shares are expected to commence trading on the Nasdaq Stock Market under the symbol “TMCR” on Wednesday, April 8, 2026.

EXHIBIT INDEX

SIGNATURE

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

Date: April 1, 2026