Manchester City have also apologised to the defender after he was struck in the face by a coin thrown during Sunday's derby which ended 3-2 to Sir Alex Ferguson's sideManchester United defender Rio Ferdinand, during their 3-2 win over Manchester City.
Ferdinand was hit by the coin as he celebrated the decisive goal, a free kick scored by Robin van Persie following a foul on Rafael on the edge of the box.
The object which hit the defender above the eye is believed to be a two pence coin, and left Ferdinand's eyebrow split open and bleeding.
The statement 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."
Shortly after the incident, a fan made his way on to the pitch and ran towards the former England international, before slipping and being restrained by Manchester City goalkeeper, Joe Hart.
An FA spokesperson added: "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.
"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."
Manchester City have also issued an apology for the behaviour of certain fans following the incidents which took place at the Etihad stadium.
A statement on their official club website read: "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.
"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."