Kleiber is a German surname. Notable people with the surname include:
Erich Kleiber (1890–1956), Austrian-German conductorMax Kleiber (1893–1976), Swiss agricultural biologist, known for Kleiber's lawCarlos Kleiber (1930–2004), Austrian conductorGünther Kleiber (born 1931), German communist politicianStanislava Brezovar or Stanislava Kleiber (1937–2003), Slovenian ballerinaJolán Kleiber-Kontsek (born 1939), Hungarian athleteDávid Kleiber (born 1990), Hungarian football player