Middle East Bank, Parsian Bank and Sina Bank have received approval from Iran's central bank to set up branches overseas, the minister, Ilse Aigner, told the newspaper.
Aigner, a member of the conservative Christian Social Union (CSU), spoke with the newspaper from Tehran during her second visit to the Iranian capital within a year.
"Business ties between Bavarian companies and Iran often fail today because of barriers in the payment process," Aigner told the newspaper in an interview published on Monday.
"That is why having branches of Iranian banks in Munich is particularly important for our businesses. Especially our small- to medium-sized firms have enormous export prospects to Iran that they will be able to utilize more easily in the future."
Many European companies complain that although U.S. sanctions against Iran over its nuclear program were lifted in January, they still cannot secure financing from Western banks because they are worried about further sanctions still in effect in the United States.
Under the nuclear sanctions, Iranian companies used methods such as transfers of funds through money changers to conduct trade, which was expensive, time-consuming and sometimes unreliable.
Aigner told the paper that the Iranian banks would now get professional help for setting up satellite offices in Munich and navigating the approval process.
She cited strong interest in exporting items to Iran from the German engineering, automotive, aerospace, environmental technology, pharmaceutical and medical technology sectors.