But the allegation is dated back to 2005 in Lambeth, the borough of London where the theater is located.
Spacey was artistic director of The Old Vic from 2004 to 2015.
But it said the same man was accused November 1 of another assault in 2008, also in Lambeth. It said numerous alleged incidents took place at the theatre - located in the borough of Lambeth - and involved members of staff.
The Met were already investigating an allegation of assault regarding Spacey against a different man in the same area in 2008.
A series of accusations have been leveled against the American since fellow actor Anthony Rapp alleged Spacey tried to seduce him when he was 14.
It opened the investigation following a stream of allegations against the actor, including testimony from Mexican actor Rob Cavazos, who worked with Spacey at the Old Vic.
Spacey said he did "not remember the encounter" but offered "the sincerest apology" if it had taken place.
"It seems that it only took a male under 30 to make Mr Spacey feel free to touch us".
Eight people have claimed that Spacey sexually harassed House of Cards employees during his time on the set, including one who he allegedly sexually assaulted.
The second allegation was made on Friday, police said.
Kate Varah, the Old Vic's executive director, issued an apology on November 16 to the alleged victims.
The BBC has contacted Spacey's legal representatives for comment.