Ferdinand appeared to be hit by a coin as he celebrated his side's third goal in their 3-2 victory at the Etihad Stadium. The defender sustained a cut just above the eye in the incident, which is now being investigated by Greater Manchester Police and the FA.
An FA statement read: "The FA is investigating the incident in which an object was thrown from the crowd and hit Rio Ferdinand following Manchester United's third goal against Manchester City on Sunday. The FA will liaise with Greater Manchester Police and await the reports of both our crowd control advisor who was present at the game and the match referee."
An FA spokesperson added: "It is disappointing that after a great game and advert for the Premier League that we are discussing this issue.
"We will work with the clubs and authorities to identify those responsible and support the strongest sanctions available, including life bans.
"We condemn any such acts and it is simply unacceptable that any player is exposed to injury in this way. To witness Rio Ferdinand leaving the field with a cut above his eye to receive treatment is appalling.
"Football in this country has made great progress over recent decades. However, we must maintain the safety and security inside of our stadia and to do this we need to isolate and identify any individuals guilty of offences with strong penalties to act as a deterrent to others."