The school was named for local businessman Frank Hume who donated adjacent land for the school's playground. Hume was a Civil War veteran who was born in Culpeper County, Virginia in 1843 and was wounded in the Battle of Gettsyburg. Hume served in the Virginia House of Delegates. Surprisingly, public schools were rare in Arlington (which was part of Alexandria County until breaking away to form its own county in 1920) until the late 19th century. A state ordinance allowing public schools was passed in 1846 by the Virginia General Assembly but no public schools seem to have been established in Arlington County until 1870; prior to that date, the public schools were situated in the southern portion of Alexandria County which became part of the City of Alexandria.
The school stood on a quarter-acre lot as seen on the 1900 Virginia Title Company map of Alexandria County. The Hume School served its South Arlington neighborhood until 1958. The building has been home to the Arlington Historical Society's (AHS) museum for decades. The AHS formed in 1956 and bought about an acre of land around the building, too, in 1960, saving the school building and an adjacent lot from development.
The Hume School was designated an Arlington County Landmark in 1978 and was listed on the National Register of Historic Places the following year. Besides being the work of a local architect, the school represents the trend away from the small schoolhouses of the 19th century to massive structures to serve the public school student. Influences of the architect's training in Boston at the Massachusetts Institute of Technology are seen in the grand design of the imposing structure. A photograph of the school-turned museum was chosen by Arlington County to grace the county car decals for 2011-2012. The school and its namesake were the subject of a presentation by Tom Dickinson of the Arlington Historical Society at a local library in 2018.