Klemm is a German surname. Notable people with the surname include:
Adrian Klemm, American Football player
Brian Klemm, American musician with third wave ska band Suburban Legends
Ekkehard Klemm, German conductor
Hanns Klemm, German aircraft pioneer and founder of the Klemm Leichtflugzeugbau GmbH (Klemm Light Aircraft Company)
Hans G. Klemm
Jon Klemm, Canadian ice hockey player
Matthias Klemm, German graphic designer
Richard Klemm
Rudolf Klemm
Walther Klemm