A German soccer federation disciplinary panel banned Hübner for "unsporting behavior" but said there was not proof of racist or discriminatory conduct. Hübner was also fined 20,000 euros ($24,300).
Following the game last week, Leverkusen defender Jonathan Tah told broadcaster DAZN that a Union player had used a derogatory term referring to Amiri's Afghan background. Tah also said he had not heard the alleged racial slur himself.
Amiri, who plays for the German national team, told a federation investigation that he could not rule out that different words might have been used, the federation said.
In a statement issued by Union, Hübner accepted the ban and fine. He said he had "cleared up" the matter after speaking with Amiri. Hübner denied using any racist language and said he had faced insulting language during the game.
Amiri told Leverkusen's club website last week that he had received and accepted an apology from an unnamed Union player for "ugly words on the pitch said in the heat of the moment that he's very sorry for."
The federation said an investigation into another Union player, Cedric Teuchert -- over alleged breaches of rules - was closed. It said Teuchert "was advised to pay closer attention to his choice of words on the field in the future."
Union won the Jan. 15 game 1-0 with a goal from Teuchert. Leverkusen is third in the league and Union is sixth.
Hübner will be banned for a visit to Augsburg on Saturday and a home game against Borussia Mönchengladbach on Jan. 30.