Born in Hanau, Germany, Hindemith was taught the violin as a child. He entered the Hochsche Konservatorium in Frankfurt am Main where he studied conducting, composition and violin under Arnold Mendelssohn and Bernhard Sekles, supporting himself by playing in dance bands and musical-comedy outfits. He led the Frankfurt Opera orchestra from 1915 to 1923 and played in the Rebner string quartet in 1921 in which he played second violin, and later the viola. In 1929 he founded the Amar Quartet, playing viola, and extensively toured Europe.

In 1922, some of his pieces were heard in the International Society for Contemporary Music festival at Salzburg, which first brought him to the attention of an international audience. The following year, he began to work as an organizer of the Donaueschingen Festival, where he programmed works by several avant garde composers, including Anton Webern and Arnold Schoenberg. From 1927 he taught composition at the Berliner Hochschule für Musik in Berlin. In the 1930s he made a visit to Cairo and several visits to Ankara where (at the invitation of Atatürk) he led the task of reorganizing Turkish music education. Towards the end of the 1930s, he made several tours of America as a viola and viola d’amore soloist.

In the 1930s the Nazis condemned his music as “degenerate”, despite protests from the conductor Wilhelm Furtwängler, and in 1940 Hindemith immigrated to the United States. (He was not himself Jewish, but his wife was.) At the same time that he was codifying his musical language, his teaching began to be affected by his theories. Once in the States he taught primarily at Yale University where he had such notable pupils as Lukas Foss, Norman Dello Joio, Harold Shapero, Hans Otte, Ruth Schonthal, and Oscar-winning film director George Roy Hill. During this time he also held the Charles Eliot Norton Chair at Harvard, from which the book A Composer’s World was extracted. He became an American citizen in 1946, but returned to Europe in 1953, living in Zürich and teaching at the University there. Towards the end of his life he began to conduct more, and made numerous recordings, mostly of his own music. He was awarded the Balzan Prize in 1962.

Hindemith died in Frankfurt am Main from acute pancreatitis.