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

May 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 FORM 6-K REPORT

Press Release and Investor Presentation

On May 6, 2026, The Metals Royalty Company Inc., a company incorporated under the laws of British Columbia (the “Company”), issued a press release titled: “The Metals Royalty Company Inc. Enters Into Definitive Agreement to Acquire a Royalty Interest on Mesabi Metallics Iron Ore Project in Minnesota”. In connection with PIPE Financing (as defined in the press release), the Company delivered an investor presentation to potential investors on a confidential basis. A copy of the press release and investor presentation are furnished herewith as Exhibit 99.1 and Exhibit 99.2, respectively, both of which shall not be deemed “filed” for purposes of Section 18 of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), or otherwise subject to the liabilities of that section, nor shall they be deemed incorporated by reference in any filing under the Securities Act of 1933, as amended, or the Exchange Act.

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: May 6, 2026