He was the son of the violinist Jan Kubelik. He studied at the conservatoire in Prague. From 1936 to 1939 and again from 1942 to 1948 he was conductor of the Czech Philharmonic Orchestra. With the rise of the Communists following World War II, he left Czechoslovakia (he became a citizen of Switzerland in 1973). He was condcutor of the Chicago Symphony Orchestra from 1950 to 1953, music director of the Royal Opera House, Covent Garden from 1955 to 1958, of the Bavarian Radio Symphony Orchestra from 1961 to 1979, and of the Metropolitan Opera, New York City, from 1972 to 1974.
Among his compositions are five operas, a number of symphonies, and chamber music.