Künneke studied musicology and literature in Berlin, and was also an advanced student of Max Bruch. He worked as a repetiteur and chorus master at a Berlin operetta theater, the Neues Operettentheater am Schiffbauerdamm, but relinquished his post as chorus master after his opera Robins Ende (1909) was premiered in Mannheim and then received productions at 38 different German opera houses. Künneke later worked under Max Reinhardt and wrote incidental music for Reinhardt’s staging of Part Two of Goethe's Faust.

Künneke only composed in order to earn a living; his true love was scholarship. He held the M . D. and Ph. D. degrees. His translation of the Anglo-Saxon epic Beowulf earned him an honorary doctorate from the University of Marburg.

Künneke's graceful music is distinguished by its rhythm and striking harmonies. His best-known work is the 1921 operetta Der Vetter aus Dingsda; many of his songs are still familiar today.

In 1926, when his operetta Lady Hamilton was premiered in Breslau (now Wrocław), he formed what would become a long friendship with the conductor Franz Marszalek. Marszalek was a dedicated advocate of Künneke's music, and during his tenure at the Westdeutscher Rundfunk in Cologne(1949-65) made numerous recordings of his works (many currently unavailable) with the Cologne Radio Orchestra and the Cologne Radio Symphony Orchestra.