Kleiber was born in Vienna. He studied in Prague and in 1923 became the music director of the Berlin State Opera in 1923.
He was known for his interpretations of the standard symphonic and operatic repertoire, as well as for championing new works. In 1925, for example, he conducted the premiere of Alban Berg's opera, Wozzeck. Later, when Berg's second opera Lulu was branded Entartete Musik (degenerate music) by the ruling Nazi Party, he resigned from his post at the Berlin Opera in protest. He later moved to Buenos Aires where he worked at the Colon Theater, and took Argentinian citizenship in 1938.
Erich Kleiber was the father of Carlos Kleiber, himself a well known conductor.