The striker was dismissed by referee Howard Webb after his arm collided with Chico Flores' face during Saturday's 2-0 win over Swansea City
Carroll was dismissed with half an hour remaining at Upton Park after the striker's arm collided with Chico Flores' face during a challenge.
Although replays showed Carroll to have made minimal contact with the top of the defender's head, referee Howard Webb showed little hesitation in producing the red card.
West Ham manager Sam Allardyce stated after the game that the club intended to challenge the decision and the Football Association confirmed an appeal had been lodged on Monday afternoon.
Carroll would miss games against Aston Villa, Norwich City and Southampton should his mandatory three-match ban be upheld.
West Ham have until 1pm on Tuesday to submit their evidence regarding their grounds for appeal.