Logan saw red after an altercation with Celtic defender Mikael Lustig.
The Swede confronted the former Manchester City youngster after he celebrated in front of the home fans following the Dons’ 1-0 win over Celtic to seal second spot in the league last weekend.
Logan appeared to strike the defender’s face during a heated confrontation, and exchanged angry words with Lustig’s team mates before he was ordered off by referee Craig Thomson.
The Pittodrie side appealed the decision, and the case was heard by an independent panel before being dismissed by the Scottish FA.
Logan will now sit out three matches for the violent conduct red.