Monuments Men Recognition Act of 2013 - Directs the Speaker of the House of Representatives and the President pro tempore of the Senate to make arrangements for the presentation of a single congressional gold medal in commemoration of the Monuments Men (men and women who served in the Monuments, Fine Arts, and Archives [MFA] Section under the Allied Armies during World War II) in recognition of their heroic role in the preservation, protection, and restitution of monuments, works of art, and artifacts of cultural importance during and following the War.

Requires the Medal's display at the Smithsonian Institution. Expresses the sense of Congress that the medal should be made available for display elsewhere, particularly at locations associated with the Monuments Men and that preference should be given to locations affiliated with the Smithsonian Institution.

Permits the Secretary of the Treasury to strike and sell duplicates in bronze of the gold medal, at a price sufficient to cover the costs of the medals.