Star Trek: Discovery actor Anthony Rapp has accused Spacey of trying to seduce him when he was 14 during a party in 1986.
Spacey said he could not remember the encounter but apologised for what he said would have been “deeply inappropriate drunken behaviour”.
Netflix said it was “deeply troubled” by the allegation and confirmed that House of Cards would end after the upcoming season.
Spacey is famous for playing ruthless US politician Frank Underwood in the hit Netflix drama House of Cards.
Many viewers have taken to Twitter to say they would feel uncomfortable see Spacey’s film American Beauty in light of the allegations.
Spacey won an Oscar for his portrayal of a middle-aged man who becomes infatuated with his teenage daughter’s friend in American Beauty.
The character, called Lester Burnham, pursues the friend, named Angela, from afar. Before the pair kiss, he tells her: “I wanted you from the first moment I saw you”.
In his Oscar acceptance speech, he said thanked his friends for pointing out his “worst qualities”.
He added: “I know you do it because you love me, and that’s why I love playing Lester, because we got to see all of his worst qualities and we still grew to love him.
“This movie to me is about how any single act by any single person put out of context, is damnable.”
Spacey starred as a deadpan crime boss, called Doc, who masterminds bank robberies in Edgar Wright’s recent film ‘Baby Driver’.
The actor is famous for appearing in the iconic mystery film The Usual Suspects from 1995. He won the Academy Award for Best Supporting Actor for his portrayal of Roger ‘Verbal’ Kint.
He is also known for appearing in 1995 film Se7en, 1997 film LA Confidential and 1994 film Swimming with Sharks.
Other films include A Time to Kill (1996), Superman Returns (2006), Beyond The Sea (2004) and Glengarry Glen Ross (1992).