If Costa accepts the charge he will serve an automatic three-match suspension with immediate effect but, if he contests it, an independent regulatory commission will rule.
Chelsea face Walsall, Newcastle and Southampton in their next three domestic fixtures.
Referee Mike Dean booked both Costa and Gabriel for their spat, before the latter was dismissed for kicking out at the Blues forward.
Gabriel and both clubs have until 18:00 BST on Thursday, 24 September to reply to their charges.
Arsenal midfielder Santi Cazorla, who was sent off for two bookable offences, has been warned about his behaviour.