The Premier League duo have been punished by English football's governing body for failing to control their players following ugly scenes at the end of Saturday's affair.
Manchester City and Chelsea have been charged by the Football Association following the late fracas that marred their Premier League encounter at the Etihad Stadium.
Chelsea overcame a half-time deficit to beat their title rivals 3-1 in Saturday's encounter, with Diego Costa, Willian and Eden Hazard on target for the league leaders.
However, the game ended on a sour note when City were reduced to nine men. Sergio Aguero was shown a straight red card for an ugly lunge on David Luiz, which earned him a four-match ban.
Aguero's tackle led to a bench-clearing melee and, following the ensuing scuffle, Fernandinho was sent off after grabbing Cesc Fabregas by the throat and pushing the Spaniard over the advertising hoardings.
The FA has taken a dim view of the incident, which occurred in the 95th minute, and has charged both clubs for "failing to ensure their players conducted themselves in an orderly fashion and/or refrained from provocative behaviour."
City and Chelsea have until December 8 to respond to the charge.
The FA also confirmed that Fabregas will face no retrospective action for his part in the coming together with Fernandinho.
Fabregas was shown seemingly tapping his opponent on the face, but a three-man panel of former elite referees decided that Fabregas' indiscretion was not worthy of a red card.
Chelsea's victory leaves them three points clear of Arsenal after 14 matches, with City four points adrift of Antonio Conte's men in fourth.
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