Tachie had rudely knocked down his opponent Fabian Greilinger in the 88th minute in the game against 1860 Munich and saw the red card from referee Nico Fuchs.
The DFB now rated the scene as a raw game and banned the 22-year-old for three games. BVB has accepted the ruling, making it legally binding.
Tachie not only missed the last game of the year against FSV Zwickau (Saturday), but also the first two games after the winter break against Waldhof Mannheim (January 17th) and Freiburg II (January 21st).
A weakening for the newcomer, the striker has so far been in the starting line-up in all 19 games and has been directly involved in nine goals.