Cleave is a surname. Notable people with the surname include:
Chris Cleave (born 1973), British journalist Egbert Cleave (fl. 1870s), American author John Cleave (born c. 1790), British chartist Mary L. Cleave (born 1947), American astronaut and engineer Maureen Cleave (1934–2021), British journalist Paul Cleave (born 1974), New Zealand author Thomas L. Cleave (1906–1983), British surgeon captain