The defender was shown a straight red card after appearing to move his head in the direction of Demirbay in the latter stages of Bayern Munich's 4-1 Bundesliga thumping of Mirko Slomka's side on Saturday.
Demirbay was booked for his part in the fracas, but Boateng will now miss the final Bundesliga match of the campaign - at home to Stuttgart on Saturday - as well as the champions' opening game of the 2014-15 season.
However, the Germany international will be available for Bayern's DFB Pokal final showdown with Borussia Dortmund on May 17.
A statement on the DFB wesbite confirmed that Boateng had been suspended for "violent conduct against his opponent in a lighter case".
Bayern's chief executive officer Karl-Heinz Rumenigge branded Boateng's dismissal "brainless", and said the former Manchester City defender could expect a heavy fine.
"Such a lack of discipline will not be accepted by Bayern Munich," he said.
"In our jersey, you have to behave respectably and if you don't hear the message, then you have to feel it (in the wallet)."
