The Citizens have retained the Premier League title after coming from two goals down to beat the Villans 3-2 at the Etihad Stadium.
However, after the full-time whistle blew, Villa boss Steven Gerrard has claimed that Olsen was "attacked" during the pitch invasion.
When asked in his post-match press conference whether his players left the pitch safely, Gerrard said: "No is the answer to that. My goalkeeper was attacked. So I think those questions should go to Pep [Guardiola] and Manchester City."
The Citizens have since released the following statement: "Manchester City would like to sincerely apologise to Aston Villa goalkeeper Robin Olsen, who was assaulted after the final whistle at today's match when fans entered the pitch.
"The club has launched an immediate investigation and once identified, the individual responsible will be issued with an indefinite stadium ban."
This is the fourth unsavoury incident within the last six days which has occurred in English football following pitch invasions.
A Nottingham Forest supporter was jailed after pleading guilty to attacking Sheffield United striker Billy Sharp on Tuesday, following a pitch invasion by Forest fans celebrating victory in the Championship playoff semi-finals.
Just two days later, Crystal Palace manager Patrick Vieira clashed with an Everton fan on the pitch at Goodison Park, while Swindon players picked up injuries after clashing with spectators following defeat on penalties against Port Vale in the League Two playoff semi-finals. body check tags ::