Domgraf-Fassbaender studied first in Berlin with Jacques Stuckgold and Paul Bruns, and later in Milan with the prominent Italian dramatic tenor Giuseppe Borgatti (who also taught the English tenor Heddle Nash).
His stage debut occurred in 1922 in his native Aachen, as Almaviva in Nozze di Figaro.
After the Second World War, he performed mostly in Vienna, Munich, Hannover, and Nuremberg, where he was resident producer at the latter city's opera house from 1953 to 1962.
In 1954, he began teaching at the Meistersinger-Konservatorium in Nuremberg, where he trained his daughter, mezzo-soprano Brigitte Fassbaender.
Domgraf-Fassbaender left a sizeable legacy of audio recordings, many of which are available on CD reissues.