"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.
"It follows an incident in the 95th minute of the game on Saturday [December 3 2016].
"Both clubs have until 6pm on 8 December 2016 to respond to the charge."
Meanwhile, Sergio Aguero has been banned for four games, the FA have confirmed.
Aguero, who was retrospectively banned earlier in the season after a clash with West Ham's Winston Reid, was sent off against Chelsea at the weekend and will now miss the games against Leicester City, Watford, Arsenal and Hull City but will be available for Tuesday's game with Celtic and the New Year's Eve clash with Liverpool.
Fernandinho, who was also dismissed against Chelsea, has received a three-match domestic ban and will be available next for the Boxing Day trip to Hull.
Fernandinho is also suspended for the game against Celtic, while Nicolas Otamendi is also out of the Leicester City clash this weekend after picking up five yellow cards - he misses just one domestic game.