The incident happened in the second half, after a coming together between the pair. Thuram stood beside defender Posch and appeared to spit into his face.
The referee didn't initially see the action, but it was captured on camera.
After Thuram had calmed down, referee Frank Willenborg reviewed the footage, and instantly brandished the red card.
Thuram could be set to face a lengthy ban for his actions.
The home side then went on to lose the game four minutes from time, as Ryan Sessegnon scored the winner to give Hoffenheim a 2-1 win.
Thuram, son of legendary Parma and Juventus defender Lillian, has been at Gladbach since 2019.