Hindemith had lived in the United States for seven years and had become a citizen when clarinetist and bandleader Benny Goodman approached him about writing a clarinet concerto. Goodman enjoyed a reputation as one of America's first great crossover successes: wildly popular as a jazz artist, he was also respected for his interpretations of the Classical clarinet repertoire. In the 1940s he commissioned important new works from a number of composers, including Bartók and Copland. He premiered Hindemith's Clarinet Concerto on December 11, 1950.

The Clarinet Concerto was written at a time when Hindemith's music was marked by a distinctive, individual tonal language encompassing the entire chromatic scale. By the late 1940s, World War II had reached its end, and the composer was prosperous, financially secure, and prolific as ever. Perhaps influenced in part by these comfortable circumstances, Hindemith invested the concerto with a particular serenity and lyricism. The work is in four movements: a sonata-allegro first movement with a surprise-laden recapitulation, a brief scherzo on an ostinato, an ever-intensifying variation movement, and a vigorous rondo finale.

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