Eight singers and a dancer claim they were sexually harassed by the Spanish tenor from the late 1980s, according to the Associated Press news agency.
Only one of the women, mezzo-soprano Patricia Wulf, agreed to be named.
Domingo has denied the accusations, and the Los Angeles Opera - which he directs - has pledged to investigate with the help of "outside counsel".
"Still, it is painful to hear that I may have upset anyone or made them feel uncomfortable no matter how long ago and despite my best intentions," continued Mr Domingo.