In a volatile end to the match at City's Etihad Stadium where Robin Van Persie clinched a 3-2 win for United, Ferdinand was left bleeding from a cut above his left eye after being struck by an object.
"Whoever threw that coin, what a shot!" Ferdinand wrote on Twitter, making light of the incident.
City said the club will assist the police with its investigation into "the throwing of missiles" and trouble between both sets of fans.
"Manchester City wishes to offer its sincere apologies to Rio Ferdinand," City said in a statement. "The club unreservedly condemns the actions which led to his being injured."
A City fan also ran toward Ferdinand, but fell and was then obstructed by City goalkeeper Joe Hart, who pushed him away. The supporter was led away from the pitch by stewards.
"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!" Ferdinand added on Twitter.
Manchester United striker Wayne Rooney was also a target for projectiles when he went to take a corner, holding up an object that had landed near him.
City said it will supply video footage and eyewitness accounts to officers to help identify the perpetrators, and then "apply its own disciplinary policies for any fans found guilty of offences."
The English Football Association launched its own investigation into the attack on Ferdinand, and called for the guilty fans to be banned from football for life.
"It is simply unacceptable that any player is exposed to injury in this way," the FA said in a statement. "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."
The Greater Manchester Police Twitter feed later received notification of racist comments directed at Ferdinand on the social networking site.
"Thank you to everyone reporting racist tweets," the force tweeted. "We are aware and are investigating."
Police are also investigating chants during the game after announcing that a man was "arrested inside stadium on suspicion of committing a racially aggravated public order offence after officers hear racist chanting."
Man City said it wasn't aware who the fan supported.
The alleged racism happened a day after a Swansea supporter was arrested at another topflight game for supposedly making a racist gesture toward Norwich defender Sebastien Bassong. The fan was released on police bail on Sunday pending further inquiries.
Rob Harris can be reached at http://twitter.com/RobHarris