Olsen was struck on the back of the head as he attempted to leave the pitch at the final whistle following City's dramatic 3-2 win.
Thousands of City fans charged onto the pitch after the final whistle, with players caught up in the mayhem and unable to reach the tunnel safely.
Villa boss Steven Gerrard said: "Our goalkeeper was attacked.
“We're going to see how he is now, but I think you should ask Pep [Guardiola] and Manchester City those questions."
City said in a 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."
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!