In 1918 Suttner moved to the Bavarian State Opera in Munich and was offered the same pay as the concertmaster. He succeeded Bruno Hoyer in the prestigious Franz Strauss chair. From 1920 to 1945 he taught at the Munich Hochschule. Heinrich Kaspar Schmid composed Im Tiefsten Walde for horn and piano, one of five pieces solo wind instruments for Suttner, in 1920. Prof. Suttner was solo horn with the Bavarian State Opera from 1918 until his retirement in 1945. His solo repertoire ranged from "Va Tacito" from Handel's opera Giulio Cesare, played on a Jagdhorn (!) to the horn concertos by Mozart, Carl Maria von Weber, Carl Matys, Richard Strauss and composers of his time. Among his solo performances with this orchestras were Mozart's second horn concerto conducted by Bruno Walter. Suttner was called the "clarinetist on the horn" due to his amazing technique and range as evidenced in his own horn concerto. He requested Richard Strauss, whom he had known for many years, to compose a second horn concerto which he dedicated to to Suttner in 1943. He played the horn part in the premiere of the trio for horn, violin and piano op.110 by Heinrich Kaspar Schmid, and the world premiere of the horn concerto by Karl Pottgiesser. Even after his retirement, he stepped in at the last minute to the Munich Opera Festival on 27 July 1947 as a solo hornist in the opera, Die schweigsame Frau (The Silent Wife) of Richard Strauss, conducted by Georg Solti, a very difficult part that he had never seen or heard previously. Over his career Suttner performed the famous "long call" from Wagner's opera Siegfried a total of 153 times, a record he still holds.

In addition to the horn concerto mentioned above, Josef Suttner himself has composed numerous pieces for horn quartet, a piece for horn and piano under the title Erinnerung sowie Etüden ("Remembrance as Etudes"), and Praktische Studien für Waldhorn (Practical studies for French horn, edited by Peter Damm, Musikverlag Bruno Uetz, BU 1220, ISMN M-50146-166-0). Suttner wrote the latter studies as an introduction to the operas of Richard Wagner. Rather than being orchestral studies in the narrow sense of the word, they are intended to acquaint the horn player with the challenges presented by Wagner's works.