Ferdinand was celebrating Manchester United's late winner in the derby when he was struck in the face by a coin from the crowd.
A club spokesperson said: "Manchester City FC security officials are co-operating fully with Greater Manchester Police in relation to events leading up to the throwing of missiles on to the field of play, and between the two sets of supporters, during today's game against Manchester United.
"Manchester City wishes to offer its sincere apologies to Rio Ferdinand. The club unreservedly condemns the actions which led to his being injured.
"GMP's review of all fan behaviour at today's match will be fully supported by the club, through the provision of CCTV footage and eyewitness accounts. Following this review, and any associated police action, the club will also apply its own disciplinary policies for any fans found guilty of offences."