The Los Angeles County District Attorney's office said the alleged incident was outside California's statute of limitations.
Officials confirmed in April that an allegation involving Mr Spacey and an incident with a man in West Hollywood in 1992 was being investigated.
Another case concerning an alleged incident in 2016 remains under review.
A number of allegations of sexual misconduct have been made against the Oscar-winning actor since last November, when he was accused by actor Anthony Rapp of making a sexual advance in 1986.
