Kurt Hessenberg came on August 17, 1908 as the fourth and youngest child of the lawyer Eduard Hessenberg and his wife Emma, nee Kugler, to the world; among its ancestors is the physician Heinrich Hoffmann, the creator of Struwwelpeter. His first music lessons, piano lessons, Hessenberg received in 1917 at the Hoch Conservatory in Frankfurt am Main, in the basic principles of harmony he was introduced to some private lessons in 1923 by the organist Karl Breidenstein. After graduation in 1927 Hessenberg went to study in Leipzig, where he studied from 1927 to 1931 at the Conservatory of composition and piano. Among his teachers were Robert Teichmüller (piano ) and Günter Raphael (composition). In 1933 he was appointed as a theory teacher at the Hoch Conservatory in Frankfurt am Main. In 1942 he joined the NSDAP (member number 8829724 ). In the final phase of the Second World War, he was informed by Hitler on the Gottbegnadeten list of the most important composers in August 1944, which saved him from a war deployment.
In 1953 he became professor of composition at the Musikhochschule in Frankfurt, later the University of Music and Performing Arts in Frankfurt am Main, where he taught until his retirement in 1973. On 17 June 1994 Kurt Hessenberg died in his native city of Frankfurt am Main.
Hessenberg is one of the most important representatives of the Protestant church music in the 20th century. Together with contemporaries such as Hugo Distler, and Ernst Pepping he proposed a radical renewal of Protestant church music. To Hessenbergs become known students count Hans Zender and Peter Cahn.