Chelsea have been fined £100,000 and Manchester City must pay £35,000 after players from both teams clashed during their Premier League meeting at Etihad Stadium earlier this month.
Tempers flared at the end of Chelsea's 3-1 win, after City's Sergio Aguero was sent off for a tackle on David Luiz.
Tempers flared at the end of Chelsea's 3-1 win, after City's Sergio Aguero was sent off for a tackle on David Luiz.
Aguero's team-mate Fernandinho was also dismissed, after grabbing Cesc Fabregas as the two teams confronted each other.
Chelsea had previously been warned they could face a points deduction.
The Premier League leaders have been fined six times since February 2015 for failing to control their players.
After the Blues were fined a record £375,000 - reduced to £290,000 on appeal - in the wake of an ill-tempered meeting with Tottenham in May, the Football Association appeal board warned "the time cannot be too far distant when... the only proper sanction is a points deduction".
However, manager Antonio Conte laughed off the possibility of a points deduction on Sunday, asking reporters if they were joking when asked if he thought the incident could harm the club's league standing.
The last top-flight teams to be docked points for disciplinary issues were Manchester United and Arsenal, in the wake of a brawl at Old Trafford in October 1990.
Manchester City manager Pep Guardiola apologised for his team's part in the confrontation after the match. Aguero, whose dismissal was his second for violent conduct this season, is banned for four games, while Fernandinho is serving a three-game suspension.
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