No, the Word museum is a common noun, a Word for any museum anywhere.
A proper noun is the name of a person, place, thing, or a title; for example:
- Museum of Modern Art, New York, NY
- National Bird Dog Museum, Grand Junction, TN
- Museum Street, Borough of Camden, London, UK
- The Academy of Motion Picture Arts and Sciences Museum
- "Terror at the Wax Museum", 1963 movie with Ray Milland and Elsa Lanchester