The 24-year-old challenged his dismissal by referee Stuart Attwell for a 64th-minute challenge from behind on striker Marouane Chamakh at the Emirates Stadium, and his case was heard by a regulatory commission on Tuesday.
An FA statement said: "At a regulatory commission hearing today, a claim for wrongful dismissal from Bolton Wanderers defender Gary Cahill was dismissed.
"As a result, Cahill's three-match suspension will remain and will be served with immediate effect."
Cahill will miss this weekend's Premier League trip to Aston Villa and the Carling Cup tie at Burnley, as well as Manchester United's visit to the Reebok Stadium.
That will come as a blow to manager Owen Coyle, who voiced his dismay at Attwell's decision in the immediate aftermath of the game.
Wanderers were pushing for an equaliser at 2-1 when Cahill departed and eventually lost the game 4-1.
Coyle said: "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."
Cahill and Coyle can at least console themselves with the fact that the commission did not view their appeal as frivolous, a finding which would have seen the player's ban extended to four games.
Source: Team Talk
Source: Team Talk