Baby is a surname. Notable people with the surname include:
Benoît Baby (born 1983), French rugby union footballer
François Baby (politician) (1768–1852), political figure in Upper Canada
François Baby (businessman) (1733–1820), Canadian businessman
François Baby (legislative councillor) (1794–1864), seigneur, businessman, and legislative councillor
Jacques Baby (1731–1789), Canadian fur trader
M. A. Baby (born 1954), Indian politician
