In an ill-tempered game, Arsenal had both Gabriel and Santi Cazorla sent off as reigning Premier League champions Chelsea won 2-0 at Stamford Bridge.
Gabriel's red card was later rescinded while Blues striker Diego Costa was later handed a three-match ban after his tussle with the Brazilian - which led to the FA charging both clubs with failure to control their players.
An FA statement read: "Following an Independent Regulatory Commission hearing, Chelsea and Arsenal have been fined Â£40,000 and Â£30,000 respectively and warned as to their future conduct after both clubs admitted a breach of FA Rule E20."
Gabriel and Costa clashed on the stroke of half-time after the Spain forward had already had an altercation with Laurent Koscielny.
After referee Martin Atkinson had initially shown both players a yellow card, Gabriel was dismissed having backed into Costa.
The FA added: " The charge was for failing to ensure their players conducted themselves in an orderly fashion from the 44th to the 47th minute of the game at Stamford Bridge on 19 September 2015
"The Independent Regulatory Commission considered the previous disciplinary records of both clubs in reaching its decision on sanction."
After Gabriel's red card, Chelsea scored twice in the second half through Kurt Zouma and Eden Hazard before Cazorla was also sent off.
Gabriel subsequently had his dismissal overturned but was still handed a one-match ban for his reaction to the decision - while Costa, who escaped immediate punishment, was suspended for three games having been found guilty on a charge of violent conduct.
Source : PA