Costa has been charged with violent conduct by the Football Association after an incident with Arsenal's Laurent Koscielny which was caught on video.
The FA has also charged Arsenal defender Gabriel with improper conduct for his behaviour after being sent off, and both Chelsea and Arsenal for failing to control their players.
Meanwhile, Chelsea defender Kurt Zouma said he was "deeply upset" after comments he made in a television interview saying team-mate Costa "likes to cheat a lot" became headline news.
Arsenal manager Arsene Wenger said Costa should have been sent off after grappling with Laurent Koscielny, pushing the defender in the face with his hands before catching him with a flailing arm, in the first half of Chelsea's 2-0 win at Stamford Bridge - the incident was not spotted by referee Mike Dean.
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 tomorrow (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.
"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.
"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.
"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 (24 September) to reply."
Costa's behaviour was also the subject of a post-match television interview with Zouma - the French defender later said on Twitter he did not mean to accuse him of cheating.
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 a clarification on Twitter on Monday 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 harsh to take Zouma's words literally.
"It's a bit harsh to take literally the words of a young player speaking in his second language immediately after a game," said the Chelsea spokesman. "Kurt is deeply upset that his words have been used to attack a team-mate and a friend."