The defender was left with blood pouring from a cut above his left eye in chaotic scenes after Robin van Persie secured United's 3-2 win at the Etihad Stadium. He had treatment but was able to complete the match.
The incident is now being investigated by Greater Manchester Police and the Football Association.
"We apologise to Rio," said a Manchester City spokesperson. "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."
Ferdinand was able to complete the game and afterwards on Twitter said: "Whoever threw that coin, what a shot! Can't believe it was a copper 2p....could have at least been a £1 coin!"
City goalkeeper Joe Hart also had to forcibly restrain a blue-clad pitch invader who was heading towards Ferdinand.
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.
"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."
Earlier in the game, Wayne Rooney was hit by a coin as he prepared to take a corner.
And police said a man was arrested in the stadium for racist chanting in another unsavoury incident.
United manager Alex Ferguson said: "It's unfortunate that a City fan runs on and coins are thrown. That shouldn't happen. The same thing happened at Chelsea, which was masked by all the other things. We could have done without that."
Referring to the incident at Stamford Bridge in October when a steward was injured by Chelsea fans when United celebrated an equally dramatic win, the Scot added: "At Chelsea, We had half a seat thrown on the pitch, coins, lighters, and nothing done about it. It's a problem."
A City spokesman said CCTV footage of the incident was being reviewed.
The crowd trouble detracted from a compelling fixture. Two Rooney goals gave United a commanding lead but City equalised through Yaya Toure and Pablo Zabaleta.
However, Van Persie, who City tried to sign in the summer, converted a dramatic free-kick in the 92nd minute, which deflected off Samir Nasri.
It was City's first Premier League defeat of the season.