The man, identified only as Mohsen V., 48, was arrested Tuesday in Frankfurt, federal prosecutors said. He holds both German and Iranian citizenship.
Customs agents searched his business premises in the city, as well as an unidentified German firm in the southwestern city of Ludwigshafen, a statement said.
Prosecutors said the deals involved items that violate trading restrictions because of their possible use "for military or nuclear purposes." They refused to elaborate.
A federal judge on Wednesday ordered that the suspect be held in custody pending possible charges.
Germany, along with the five permanent members of the U.N. Security Council, has been at the forefront of efforts to address concerns over Iran's nuclear ambitions.
Tehran has defied Security Council demands to halt uranium enrichment, which could be used both to generate nuclear power and to create the fissile core of warheads. It insists its program has purely peaceful purposes.