S.Oliver Würzburg sacked Douglas Spradley on Friday after two and a half years.
In November 2015, Bauermann signed a four-year contract extension until 2019 with Iran basketball federation.
The German coach has sent an email to the Iranian federation and said he stepped down from his role due to his three-year-old child.
Iran has not yet announced replacement for Bauermann.
Bauermann has worked at DBB, Bayern Leverkusen, Brose Bamberg and the FC Bayern, and Krasny Oktyabr Volgograd in Russia before being named as Iran coach.