The setback means Bayern have slipped further behind in the race to finish in at least third place, which is qualifies them for a Champions League place next season.
Robben, Bayern's play-maker, was furious after his team conceded a late equaliser which saw them drop to fourth in the German league on Saturday.
A subsequent dispute with the match referee, during which an irate Robben claimed Bayern should have been awarded a penalty earlier in the match, earned him a red card.
The disciplinary commission of the German Football Federation (DFB) announced Robben's ban Monday, adding to his woes by slapping him with a €15,000 fine.
Robben's last dismissal was in March 2006 while playing for Premier League side Chelsea against West Bromwich Albion.
He will now miss league matches against Bayer Leverkusen on Sunday and Frankfurt the following week.
On Sunday Bayern sacked their coach Louis van Gaal, with the ousted Dutchman's assistant Andries Jonker taking over as caretaker head coach for the remainder of the campaign.
Bayer Leverkusen's coach Jupp Heynckes has already been announced as Bayern's manager for next season.