Birger Eyolf Kleven (February 27, 1908 - February 8, 1989) was a Danish amateur football (soccer) player, who played 30 games and scored eight goals for the Denmark national football team from 1930 to 1942. Born in Copenhagen, Kleven played as a midfielder for AB from 1927 to 1944.
He is the younger brother of fellow Danish international Arne Kleven.