George Gustav Heye was a wealthy New York investment banker who began collecting Native American objects in 1903 - traveling through North and South America, buying artifacts at any opportunity, sometimes employing field agents to collect for him. By the time he opened his Museum of the American Indian on Audubon Terrace in upper Manhattan in 1922, the collection numbered hundreds of thousands of objects. By his death in 1957, it had grown to nearly a million. The collecting methods were not all ethical - Heye and his agents acquired objects through purchases, gifts, archaeological excavation, and at times through methods that would not pass present-day legal or ethical scrutiny. The collection nonetheless preserved an enormous amount of Indigenous material culture at a time when many Native communities were being pushed off their land. The Heye Foundation operated the museum independently in Manhattan for seven decades, but by the 1980s it was failing financially and seeking a new home.

In 1989, Senator Daniel Inouye of Hawaii introduced the National Museum of the American Indian Act after a controversy revealed that the Smithsonian held between 12,000 and 18,000 sets of Native American human remains in its various collection storage facilities, most never displayed. Tribal leaders had been increasingly demanding return of those remains, along with sacred objects and objects of cultural patrimony. Inouye's bill, passed as Public Law 101-185, did three things: it transferred the Heye collection from New York to the Smithsonian, it chartered a new National Museum of the American Indian, and it required the Smithsonian to consider human remains, funerary objects, sacred objects, and cultural patrimony for repatriation to tribal communities. Since 1989, the Smithsonian has repatriated more than 5,000 sets of individual remains - roughly one-third of the original total. The 1990 Native American Graves Protection and Repatriation Act extended similar requirements to all federally funded institutions.

The museum operates as three facilities. The original Heye Center reopened in October 1994 in lower Manhattan at the Alexander Hamilton U.S. Custom House - a Beaux Arts-style building completed in 1907 by Cass Gilbert, designated a National Historic Landmark, occupying about 20,000 square feet on two floors. The Cultural Resources Center, opened in 2003 in Suitland, Maryland, is a nautilus-shaped building that houses the bulk of the collection, the library, and the photo archives. The National Mall building - the most prominent of the three - opened on September 21, 2004. Together the three facilities hold approximately 825,000 objects, about 85 percent of which came from the Heye Collection.

Douglas Cardinal won the design competition in 1993. His proposed building, intended to evoke rock formations shaped by water and wind, was unlike anything else on the Mall - curving walls, no sharp corners, an east-facing entrance, a 120-foot-high central space for contemporary Native performances. The exterior cladding is Kasota limestone from Minnesota, a golden-colored stone whose hue and texture suggest natural sandstone formations. Around the building, designer Donna House supervised the planting of nearly 30,000 native plants representing four Indigenous-managed ecosystems: woodlands, wetlands, croplands, and a hardwood forest. Disagreements during construction led to Cardinal being formally removed from the project before completion - but the building retains the entirety of his original design intent, and he continued providing input during construction. GBQC Architects of Philadelphia, Jones and Jones of Seattle, and SmithGroup of Washington completed the project. The Hopi designer Ramona Sakiestewa and Caddo consultant Lou Weller contributed to the design as well.

Outside the museum, the National Native American Veterans Memorial opened on Veterans Day 2020 in a virtual ceremony. The formal dedication ceremony took place on November 11, 2022, with a procession of more than 1,500 Native veterans from more than 120 Native nations. The memorial - titled Warriors' Circle of Honor and designed by Cheyenne and Arapaho artist Harvey Pratt - is a vertical steel circle standing on a stone drum, surrounded by benches engraved with the logos of the military branches. Four stainless steel lances stand around the benches, where visitors can tie cloths for prayer and healing. Inside the museum, the Mitsitam Native Foods Cafe serves food from five culinary regions - Northern Woodlands, South America, Northwest Coast, Mesoamerica, and Great Plains. Its founding executive chef Freddie Bitsoie is Diné. Cynthia Chavez Lamar, an enrolled member of San Felipe Pueblo, became museum director in February 2022 - the first Native American woman to direct any Smithsonian museum. The human remains vault is smudged weekly with tobacco, sage, sweetgrass, and cedar. Sacred Crow objects in the Plains vault are smudged with sage during the full moon.