Kleiber is a German surname. Notable people with the surname include:
Erich Kleiber (1890–1956), Austrian-German conductor
Max Kleiber (1893–1976), Swiss agricultural biologist, known for Kleiber's law
Carlos Kleiber (1930–2004), Austrian conductor
Günther Kleiber (born 1931), German communist politician
Stanislava Brezovar or Stanislava Kleiber (1937–2003), Slovenian ballerina
Jolán Kleiber-Kontsek (born 1939), Hungarian athlete
Dávid Kleiber (born 1990), Hungarian football player