The FA said on its website that Costa had been charged with an alleged "act of violent conduct" after television replays showed him catching Arsenal defender Laurent Koscielny with his arm in an incident not spotted at the time by the referee.
"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," an FA statement said.
"For retrospective action to be taken, and an FA charge to follow, the decision by the panel must be unanimous."
Brazilian defender Gabriel, who was sent off after tangling with Costa shortly after that incident, was charged with "improper conduct" following his straight red card which Arsenal have since appealed against.
Spain international Costa has until 1700 GMT on Tuesday to respond to the charges while Gabriel has until 1700 GMT on Thursday to respond.
Both Chelsea and Arsenal were also charged by the FA for failing to control their players.
Chelsea won the fractious game 2-0 with Arsenal ending the match with nine men after Santi Cazorla was also dismissed for a second yellow card after a foul on former Arsenal midfielder Cesc Fabregas.
Arsenal manager Arsene Wenger was critical of Costa after the derby, saying he is "always involved in provocation".