With around 15 minutes left and hosts Augsburg defending a 1-0 lead, midfielder Baier went to ground close to the Leipzig technical area.
As he got up, he made an obscene gesture in the direction of Hasenhuttl and also appeared to spit in his direction.
The coach then refused to shake hands with 33-year-old Baier.
The German FA (DFB) fined the Augsburg captain €20,000 for unsporting conduct, and imposed a one-game ban that means he misses the weekend trip to Stuttgart.
Before the punishment was announced, Baier used Instagram to say he "apologised to all those who felt offended" by his gesture.