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.
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.
The thing that bugs me about these are the pitiful amounts clubs have to pay in fines. Both sides wouldn't miss a few million quid. Fine them according to their wealth imo. Imagine what the FA could do with 5 million quid in fines because two clubs had a bit of handbags. Imagine how many grassroots clubs would benefit from it
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