The charge follows the mass fracas in the 95th minute of the game at Etihad Stadium, which Chelsea won 3-1.
City had forward Sergio Aguero and midfielder Fernandinho sent off, but Chelsea midfielder Cesc Fabregas will not face any further action.
City manager Pep Guardiola apologised for his team's part in the incident.
Aguero, 28, received a four-match ban for what was his second dismissal for violent conduct this season, following a high and late challenge on Chelsea defender David Luiz.
Fernandinho clashed with Fabregas in the scuffle that followed Aguero's challenge, and the Brazil midfielder will serve a three-match ban.
Both clubs have until 18:00 GMT on 8 December to respond to the charge.
Manchester City and Chelsea have been charged by the Football Association for failing to control their players during the Premier League game on Saturday.