The alleged assault took place in London.
The alleged victim came forward on November 17 following the Old Vic's investigation into Spacey's conduct while he was artistic director of the theatre.
The American actor is facing numerous claims of sexual assault and harassment, as part of a broader scandal in Hollywood sparked by allegations against mogul Harvey Weinstein. It said numerous alleged incidents took place at the theatre - located in the borough of Lambeth - and involved members of staff.
The allegations against Spacey started with Star Trek actor Anthony Rapp.
The incidents reported to the Lambeth theatre cover a period of 1995 to 2013 and have not been verified, The Old Vic said. It's unclear, however, if the latest allegation is connected to the theater's internal investigation. These allegations have been a shock and a disturbing surprise to many of us.
"It seems that it only took a male under 30 to make Mr Spacey feel free to touch us".
In the past few weeks Spacey has been fired from the Netflix TV series "House of Cards", was dropped by his talent agency and publicist and is being cut out of Ridley Scott's finished film "All the Money in the World". But it also acknowledged that the Oscar-winning actor's stardom had created a "cult of personality" that discouraged any alleged victims or witnesses of misconduct to make their complaints known.
This allegation was brought to the attention of police last Friday.
The BBC has contacted Spacey's legal representatives for comment.
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