Groover is an English surname. Notable people with the surname include:
- Denmark Groover Jr. (1922–2001), American politician
- Gino Groover (born 2002), American baseball player
- Jan Groover (1943–2012), American photographer
- John Groover, Jr., musician with the band The Futuristiks
- Wink Groover (1935–2010), American horse trainer
Notable places named after people with the surname include:
- Groover-Stewart Drug Company Building in Florida
- Hatcher-Groover-Schwartz House in Georgia