The English centre-back was left with blood pouring from his face after being hit by a missile apparently thrown from the crowd in the aftermath of Robin van Persie's injury-time winner for United at the Etihad Stadium.
Greater Manchester Police have launched an investigation into the incident, while City expressed regret to Ferdinand.
"We apologise to Rio," said a spokesman from the club.
"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 himself made light of what had happened, writing on Twitter: "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!"
City manager Roberto Mancini claimed not to have witnessed the incident, but he condemned it nonetheless.
"I didn't see, so I don't know what happened," said the Italian.
"We have fantastic support but we can't do what that person did, because it's not good."
A fan wearing City colours also had to be restrained by home goalkeeper Joe Hart after walking onto the pitch and making his way towards Ferdinand after van Persie's goal.
City had not lost a home game in the Premier League for two years and their defeat saw United establish a six-point lead at the top of the table.
Source: AFP