Mounsey is a surname. Notable people with the surname include:

Ann Mounsey (1811–1891), British organist and composer Augustus Henry Mounsey (1834–1882), British diplomat Elizabeth Mounsey (1819–1905), British organist and composer, sister of Ann Rob Mounsey (born 1952), American musician, composer, and arranger Tara Mounsey (born 1978), American ice hockey player William Mounsey (disambiguation), multiple people