His role in All the Money in the World is to be recast and his scenes reshot. The release is expected to go ahead as planned on 22 December.
Spacey, who was late oil tycoon Jean Paul Getty in the film, will be replaced by Christopher Plummer.
The claims against Spacey span from the mid-1980s to last year.
All the Money in the World, directed by Ridley Scott, is about the 1973 kidnapping of Getty's teenage grandson.
Variety said that Spacey had shot about two weeks of footage and there were many scenes in the film where he was the only actor on screen.