Cibber is a surname. Notable people with the surname include:
- Caius Gabriel Cibber, Danish sculptor; father of Colley Cibber
- Charlotte Cibber, English actress, playwright, novelist, autobiographer, and noted transvestite
- Colley Cibber, British actor, playwright, and Poet Laureate; father of Charlotte and Theophilus Cibber
- Susannah Maria Cibber, English singer and actress; wife of Theophilus Cibber
- Theophilus Cibber, English actor, playwright and author