The former Chelsea man has also been fined 15,000 euros having been shown the red card after full-time following an angry confrontation with officials.
Robben marched towards the referee to complain of a perceived injustice shortly after the final whistle as Bayern dropped two points - drawing 1-1 with lowly Nuremberg - and so slipped out of the Champions League places.
Marching orders: Bayern Munich's Arjen Robben was shown a red card after the match following an angry confrontation with the referee
The 27-year-old believed his side should have been awarded a penalty earlier in the match, but his claims fell on deaf ears, so too has his subsequent apology to both the referee and his club.
AC Milan forward Zlatan Ibrahimovic was also sent off for a similar offence in his side's Serie A win on Sunday.
The disciplinary commission of the German Football Federation (DFB) announced Robben's ban on Monday.
Robben will sit out next weekend's crunch clash against second-placed Bayer Leverkusen followed by their match against Eintracht Frankfurt.
Slip up: Despite leading through Thomas Mueller, Bayern conceded late on to fall out of the Champions League spots
Bayern are fourth in the Bundesliga, a point behind Hannover who currently occupy the final Champions League place. Borussia Dortmund sit on top of the pile a further 13 points ahead.
It is the Dutchman's first red card since moving to the Alianz Arena, with his last red card coming five years ago in Chelsea blue against West Bromwich Albion.
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