Blues striker Costa has been charged with violent conduct and Gunners defender Gabriel with improper conduct after the pair were embroiled in a few headed exchanges during the reigning Premier League champions' 2-0 win at Stamford Bridge on Saturday.
It has also been confirmed that Arsenal will appeal the red card given to Gabriel for his reactionary 'kick' on Costa on the stroke of half-time while both clubs have been charged for failing to control their players.
A statement from the FA read: "Diego Costa has been charged for an alleged act of violent conduct which was not seen by the match officials but caught on video.
"Off the ball incidents which are not seen at the time by the match officials are referred to a panel of three former elite referees.
"Each referee panel member will review the video footage independently of one another to determine whether they consider it a sending-off offence. For retrospective action to be taken, and an FA charge to follow, the decision by the panel must be unanimous.
"Finally, both clubs have been charged for failing to control their players under FA Rule E20.
"Both clubs and Gabriel have until 6pm on Thursday [September 24] to reply."
Arsenal's official website added: "…the club can confirm that it is appealing wrongful dismissal and the three-match ban given to Gabriel."