City striker Sergio Aguero committed a reckless tackle on Chelsea defender David Luiz during stoppage time, sparking a melee at the Etihad Stadium with players and coaching staff from both teams involved in ugly scenes.
"Both Manchester City and Chelsea have been charged for failing to ensure their players conducted themselves in an orderly fashion and/or refrained from provocative behaviour," the FA said in a statement.
"Both clubs have until 6pm on 8 December 2016 to respond to the charge."
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Aguero and City midfielder Fernandinho were sent off and will serve four and three-game bans respectively.
Leaders Chelsea won the match 3-1 to move four points clear of fourth-placed City in the table.
(Reporting by Ed Osmond, editing by Alan Baldwin)
