The current La Liga holders snatched all three points on Saturday (October 18) thanks to a 93rd minute goal from defender Ronald Araujo.
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As emotions ran high, Flick, 60, argued with officials about the number of minutes added at the end of the game, and saw red as a result.
Flick will now be forced to watch on from the stands in the first El Clasico of the season at the Santiago Bernabeu on October 26th.
Barcelona are currently one point ahead of Xabi Alonso’s side in the race for the title, although Real Madrid have a game in hand.