Spann is a surname. Notable people with the surname include:
Alexi Spann, American breaststroke swimmer
Antwain Spann, American football player
Gloria Carter Spann, sister of former American president Jimmy Carter
James Spann, American meteorologist
Johnny Micheal Spann, Central Intelligence Agency paramilitary operations officer
Joseph E. Spann Jr., American Historian and Genealogist, author of Spann's Guide to Gibson 1902-1941
Othmar Spann, Austrian philosopher
Otis Spann, American blues musician
Scott Spann, American swimmer
Silvio Spann, Trinidad and Tobagan footballer