The Museum grew out of a number of earlier initiatives at Monash University, starting in 1961 when the inaugural Vice Chancellor Louis Matheson created a fund for the purchase of artworks by then living Australian artists.

[1] In the late 1960s John Waterhouse and Patrick McCaughey (then a teaching fellow at Monash and art critic at The Age) were appointed as curators, and in 1975, McCaughey created the Monash University Gallery on the seventh floor of the Menzies Building of the main campus and set up an artist-in-residence program.

[1] The museum aims to support "innovative art-led models of interdisciplinary teaching, learning and research across the University".

An example of this is Weelam Ngalut (Our Place), created by Quandamooka artist Megan Cope in 2109, designed to welcome students and visitors onto Kulin country.

[15] Set between two buildings on Dandenong Road is the art installation Silverscreen by Callum Morton which serves as ceremonial entry into the MUMA precinct.