After the club secured its fourth Premier League crown in five years, home supporters at the Etihad Stadium spilled onto the pitch in celebration.
A television broadcast of the game appears to show a spectator making contact with the back of Olsen’s head as the Villa keeper was being escorted off the field.
“Manchester City would like to sincerely apologize to Aston Villa goalkeeper Robin Olsen, who was assaulted after the final whistle at today’s match when fans entered the pitch,” said a statement from the club.
“The Club has launched an immediate investigation and once identified, the individual responsible will be issued with an indefinite stadium ban.”
In a postgame press conference, Villa manager Steven Gerrard was asked by reporters if the club’s players had safely exited the pitch.
“No is the answer to that,” Gerrard replied.
“My goalkeeper was attacked. So I think those questions should go to (manager) Pep (Guardiola) and Manchester City.”
According to Sky Sports News, Aston Villa said in a statement that Olsen was “completely fine” after the incident, adding that he did take a hit to the back of the head.
The club said it is unsure if the incident happened on purpose and would not be making a complaint, Sky reported.
CNN has contacted Aston Villa and the English Football Association (FA) for comment.
Guardiola was asked about the incident after the match, saying: “I am so sorry … I am so sorry on behalf of the club for Olsen and Aston Villa.”
The City boss said he didn’t know the intentions behind the action, but added: “It’s always difficult to understand why people react in that way, how (they) cannot celebrate themselves, be happy and not do these kind of things.
“I don’t know how (to stop it) … You cannot put 1,000 guards or police to control there. We are so sorry. It’s the bad news of today.”
“Both have been bailed ahead of the court appearances,” said a police statement.
“Enquiries into the reported assault of a player on the pitch after the final whistle are ongoing with officers working in partnership with both football clubs.”
That was after hundreds of spectators invaded the pitch at Goodison Park in Liverpool after Everton avoided relegation from the Premier League with a 3-2 victory over Crystal Palace.