The reigning champions lost 3-2 at the Etihad Stadium after Robin van Persie netted a late winner for United which was celebrated with vigor by Ferdinand who received a cut above his eye after being struck with the coin.
City will now find out who is responsible for the act whilst apologizing to Ferdinand for what occurred.
"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."