The singer-songwriter said he has already started work on the new project, an ambition since his early teens.
Variety quotes him as saying: "I've wanted to write an opera since I was about 14 years old. But I couldn't find a story that I could wrap my head around."
Talking about his inspiration for the show, he said: "The construct of the diva, from Maria Callas to Norma Desmond, and the movie Diva from the '80s. And God darn it, there's a bit of me in that too."
Wainwright will be both composer and librettist for Prima Donna, which has been commissioned by the Metropolitan Opera.
He said it will tell the story of "a day in the life of an opera singer".