It was the first European lender to do so since sanctions were eased following the 2015 pact between Iran and world powers.
However, since then the bank has not extended any funding, citing legal uncertainty.
On Tuesday US President Donald Trump announced the US withdrawal from the “disastrous” agreement and the reimposition of sanctions on Iran.
Oberbank said it would have to wait for further details of the deal’s future and the next US moves before deciding on whether it could eventually begin providing credit.
“We have to think of the security of our clients,” Oberbank spokesman Frank Helmkamp told AFP, pointing to the danger of falling foul of US sanctions on businesses that have dealings in Iran.
In response to Trump’s move the other parties to the agreement have said they will try to keep it functioning.
The foreign ministers of France, Britain and Germany are due to meet Iranian representatives next Monday “to consider the entire situation,” France’s Foreign Minister Jean-Yves Le Drian told RTL radio on Wednesday.
Oberbank’s statement reflects the general caution over financial firms’ dealings with Iran and especially now after Trump’s move.