Cahill was dismissed for his foul from behind on Gunners striker Marouane Chamakh after 64 minutes of the Emirates Stadium clash.
Arsenal, who led 2-1 at the time, went on to win the match 4-1.
The appeal will be held by a regulatory commission on Tuesday, the FA announced.
Bolton manager Owen Coyle was disappointed by referee Stuart Attwell's decision to judge the foul as a sending-off offence, saying on Saturday: "I don't think it merited a red.
"All of a sudden we were playing Arsenal with 10 men, and it is difficult at the best of times with 11.
"We had put so much into the game that at that time we looked like the team who would get the equaliser."