Costa has been cited for an incident involving Gunners defender Laurent Koscielny in his side's 2-0 win at Stamford Bridge, with the Blues given until 6pm on Tuesday to respond.
The case for the defence became a little murkier on Monday when Chelsea defender Kurt Zouma was forced to explain comments in a television interview that the Spain striker "likes to cheat a lot".
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Arsenal have already signalled their intent to appeal against Gabriel's dismissal in the match, but he has also been handed a separate charge of improper conduct.
Both London clubs face charges of failing to control their players, with a reply deadline of 6pm on Thursday.
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The FA said in a statement: "Diego Costa has been charged for an alleged act of violent conduct which was not seen by the match officials but caught on video.
"The Chelsea forward was involved in an incident with Arsenal's Laurent Koscielny in the 43rd minute of the game. He has until 6pm (on Tuesday) to reply.
"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."
Costa's behaviour was the subject of a post-match television interview with the aforementioned Zouma, during which the French defender made potentially inflammatory comments that both he and the club attempted to clarify on Monday.
The 20-year-old told beIN Sports: "Everyone knows Diego and this guy likes to cheat a lot and put the opponents out of his game, and that happened in the game.
"He's a real nice guy in the life and we are very proud to have him."
Zouma posted an explanation on Twitter saying: "Sorry for any confusion, English is not my first language & I did not mean to accuse anyone of cheating. Simply to say Diego is a player who puts pressure on his opponents & who I have huge respect for."
A Chelsea spokesman said it was unfair to take Zouma's words at face value.
"It's a bit harsh to take literally the words of a young player speaking in his second language immediately after a game," the Chelsea spokesman said. "Kurt is deeply upset that his words have been used to attack a team-mate and a friend."
Regarding Gabriel, the FA statement continued: "Arsenal defender Gabriel has been charged with improper conduct for his behaviour following his dismissal, whilst team-mate Santi Cazorla has been warned for his behaviour following his sending-off.
"Both clubs have been charged for failing to control their players under FA Rule E20."
Arsenal said they would appeal for both wrongful dismissal in relation to Gabriel and the length of his ban.
A statement read: "The club can confirm that it is appealing wrongful dismissal and the three-match ban given to Gabriel."