Monday's ruling by the German Football Association (DFB) follows Linke's sending off for elbowing an opponent in the German champions' 2-0 defeat by Schalke 04 on Saturday.
Linke has also accepted a fine by his club for the offence, the amount of which was not revealed.
The ban only applies to the Bundesliga and Linke is available for Wednesday's Champions League game at home to Olympique Lyon.
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