The FA have also charged both teams with failure to control their players during the melee
Sergio Aguero will miss upcoming games against Arsenal and Premier League champions Leicester City after being hit with a four-game ban following his red card against Chelsea.
The Argentinian was dismissed in the 90th minute of the game after a reckless challenge on David Luiz, which saw him lunge into the outstretched leg of the Brazilian.
He was given a straight red card and the tackle also led to players from both sides getting caught in a melee at the end of an ill-tempered game.
Manchester City's Fernandinho was also dismissed for his part in the clashes after pushing Cesc Fabregas. He has been handed a three-game ban for the straight red card.
Players from both sides were involved in a scuffle at the end of Saturday's early game at the Etihad Stadium. Image: Martin Rickett PA Wire/PA Images
Chelsea's 3-1 win at the Etihad Stadium constituted their eight in-a-row and leaves them comfortably at the top of the Premier League table.
Fernandinho will be available to return for their St Stephen's Day clash with Hull City.
This is the second time this season Aguero will have to serve a ban for violent conduct. Earlier in the year, he was cited by the FA for an apparent elbow on West Ham's Winston Reid and was forced to serve a three-game suspension.
The FA have also charged both teams with failure to control their players during the melee. Both clubs have until 6pm on Thursday to respond to the charges.