The museum was first proposed by a prominent local lawyer and educator, Juan Bautista Terán [es], who in 1912 established the National University of Tucumán.
The museum was conceived to complement the new university's School of Fine Arts, and on June 18, 1916, the institution was inaugurated as the first in the city of San Miguel de Tucumán.
It was again transferred in 1957 to the historic home of former President Nicolás Avellaneda, though the building's deteriorating state led to the museum's closure in 1997, and its collections were temporarily moved to the provincial Secretariat of Culture.
The closure of a landmark branch of the Bank of the Province of Tucumán and its designation as a National Historic Monument allowed the Secretariat of Culture to relocate the growing collections to its present site, reinaugurating the museum on September 29, 2003.
The museum is housed in an eclectic, baroque and French neoclassical building designed in 1905 by Belgian-Argentine architect Alberto Pelsmaekers (1855 – 1923).