The building that houses the museum was originally the home of the Penang Free School, the oldest English-medium school in Southeast Asia, founded in 1816. The school occupied the site until 1927, after which the building served various administrative purposes.
During World War II, the building suffered significant damage when its eastern wing was destroyed by Allied bombing. In 1964, it was officially opened as the Penang State Museum by the first Governor of Penang. Today, the Farquhar Street branch focuses on the historical evolution of Penang—featuring galleries on the multi-ethnic communities, the colonial era, and the Japanese occupation—while its sister branch on Macalister Road serves as the dedicated State Art Gallery.