The FA dismissed a claim from the Gunners following his red card in Saturday's Premier League game at Newcastle.
The 24-year-old Ivory Coast forward was sent off in the second half of the goalless draw at St James' Park for striking Magpies midfielder Joey Barton following what the home side claimed was a dive in the penalty area.
On Monday, the Gunners lodged a claim that the standard three-game ban was "clearly excessive", but an FA regulatory commission heard the case on Tuesday and ruled that the punishment should stand.
"Arsenal's Gervinho has had his three-match suspension for violent conduct confirmed today," read an FA statement.
"The player was sent off during Arsenal's fixture against Newcastle United at St James' Park on Saturday.
"Arsenal subsequently lodged a claim that the standard punishment of three matches was clearly excessive.
"A commission heard the claim today and dismissed it, meaning the player must serve a three-match suspension with immediate effect."
On Monday, the FA charged both clubs with failing to control their players following the ill-tempered opening fixture on Tyneside.
Arsenal midfielder Alex Song faces a separate charge of violent conduct after his stamp on Barton, which had inflamed the situation, was missed by referee Peter Walton.
Gervinho will miss the games against Liverpool, Manchester United and Swansea - and Song could also be hit by the same retrospective punishment.
Barton, meanwhile, received a yellow card for his part in the melee, and as such has already been sanctioned.
The controversial midfielder admitted on Twitter that he "went down easily" following Gervinho's slap.