Mushet is a surname. Notable people with the surname include:
David Mushet (1772–1847), Scottish engineer and metallurgist Robert Mushet (writer) (1782–1828), Scottish official of the Royal Mint, and writer on financial topics Robert Forester Mushet (1811–1891), British metallurgist and businessman Robert Mushet (cricketer) (1901–1992), Scottish cricketer