Munch was born in Strasbourg. He had a career as a violinist, being leader of the Leipzig Gewandhaus Orchestra under Wilhelm Furtwangler from 1926 to 1933, before making his conducting debut in Paris. He was principal conductor of the Boston Symphony Orchestra from 1949 to 1962, becoming the first to take them overseas. In 1967 he founded the Orchestre de Paris. He died in Richmond, Virginia while on an American tour with them.