He founded and endowed the Museum of the American Indian in 1916, and it opened in 1922, in a building at 155th Street and Broadway, part of the Audubon Terrace complex, in the Sugar Hill neighborhood, just south of Washington Heights.

[5] For the past ten years, the museum had wished to relocate because its Upper Manhattan facility was insufficient, and the Custom House was being offered as an alternative for the museum's possible relocation to Washington, D.C.[6][7] Mayor Ed Koch and U.S. senator Al D'Amato were initially opposed to Moynihan's plan, but dropped their opposition by August 1987.

The Heye Center offers a range of exhibitions, film and video screenings, school group programs and living culture presentations throughout the year.

Organized by geographic regions (including Central and South America), the exhibit displays over 700 items and crosses the line from ethnology to art.

The ground floor of the building houses the Diker Pavilion for Native Arts and Culture[21] and the imagiNATIONS Activity Center,[22] opened in 2018.