The German soccer federation, which opened investigatory proceedings against Baier on Wednesday, suspended the player and fined him 20,000 euros ($24,000) for making the gesture "with his right hand in the direction of the Leipzig coaching area."
Referee Daniel Siebert did not see the gesture, but Baier agreed to the sanction after he was summoned to give his side of events. Baier approached Hasenhuettl after his team's 1-0 win but the Leipzig coach refused his handshake.
"It wasn't an apology. You saw the action on TV. I don't need to comment on it or judge it," Hasenhuettl said after Augsburg's 1-0 win. Baier apologized to teammates on social media and said he also tried to apologize in the Leipzig changing room after the game.
"I did not do justice to my role as Augsburg captain," Baier said. "On the spur of the moment I allowed myself make a gesture that I myself don't know how I made. I apologize to all who took offense from it."