City, for their part, have apologised to Ferdinand in a statement and promised to take appropriate action.
"Manchester City FC security officials are co-operating fully with Greater Manchester Police in relation to events leading up to the throwing of missiles onto the field of play, and between the two sets of supporters, during today's game against Manchester United," it read.
"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."
The Football Association later issued their own statement that 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.
"An FA spokesperson said: '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.