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."
Manchester City apologised to Ferdinand shortly after the match and denounced the actions of the supporter.
"We apologise to Rio," a Manchester City spokesperson said. "We condemn the actions of the individual concerned. We are reviewing the CCTV with the police and our normal security.
"We will support the police with any investigation and hopefully identify the person as soon as possible."
After Ferdinand was struck by the object, a Manchester City fan ran onto the pitch in the England defender's direction.
He slipped and fell to the ground as he approached Ferdinand but was then obstructed by City goalkeeper Joe Hart who pushed him away.
The supporter was then led away from the pitch.
When Ferdinand, who was able to complete the match, left the pitch after the final whistle he was seen to have an object in his hand which he showed to referee Martin Atkinson before he threw it to the ground.
A message on Ferdinand's official Twitter account posted at 4.34pm read: "what a result,3points! Sweet! Whoever threw that coin,what a shot! Can't believe it was a copper 2p....could have at least been a £1 coin!"
He later added: "Respect to Joe Hart for protecting that idiot who ran on!! Love the banter between fans but there is a point when it goes too far...calm it!"
Sir Alex Ferguson adopted a more serious tone when questioned about the incident afterwards.
"It was disappointing when the supporter ran on the pitch and Rio got hit in the eye by a coin," he said. "The game didn't deserve that.
"The same thing happened at Chelsea which was masked really by all the other things that happened.
"But, you know, two fantastic teams today, I think, and a fantastic game of football, and it could do without that."
The violent scenes were in contrast to earlier in the match.
According to Greater Manchester Police's (GMP) Twitter feed, there had only been one arrest by 2pm of a suspected ticket tout outside the stadium.
However, during the game GMP announced that another man was arrested inside the ground on suspicion of committing a racially aggravated public order offence after officers heard racist chanting.
Earlier, the match commander Supt Craig Thompson said: "I have every confidence this match will mirror the two derbies last season and the football will be the only talking point.