The player made the gesture in the 74th minute of Tuesday's 1-0 win over Leipzig. He attempted to shake hands with the coach at the end of the match but Hasenhuettl refused.
Baier later apologised and said the gesture had been made in the heat of the moment.
"Referee Daniel Siebert said when asked about it that he did not see it during the match and that is why the DFB disciplinary commission started investigating later," the DFB said in a statement.
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"The player has been banned for one game for his extremely unsporting behaviour. He also has to pay a fine of 20,000 euros."
The player had already accepted the verdict, the DFB said.
(Reporting by Karolos Grohmann; Editing by Toby Davis)
