Mieg is a Spanish surname. Notable people with the surname include:
(1731–1799), Swiss physician and botanist. François Thierry-Mieg (1908–1995), a high-ranking member of Bureau Central de Renseignements et d'Action (BCRA) (1780–1859), Swiss professor and naturalist who arrived in Spain Miguel Mieg (1896–1981), Spanish footballer Peter Mieg (1906–1990), Swiss composer, painter, and journalist (1844–1935), Spanish teacher and volapükist