The state-affiliated Jaame-jam newspaper reported that the yet-unidentified German national took photos of "sensitive oil centers" at the Aghajari oilfield.
The Tasnim news agency and the Student News Network, both close to Iran's paramilitary Revolutionary Guard, also reported the person had been taking photos of the oil facility, without providing any further details.
Germany's dpa news agency reported that the German Foreign Ministry is aware of the reports and its embassy in Tehran is working to clarify the situation.
The arrest reports come a day after Germany summoned the Iranian ambassador to protest Tehran's handling of demonstrations.
Iran security on alert amid protests
Iran's security service have been on high alert amid months of political turmoil following the death of a young woman, 22-year-old Mahsa Amini, at the hands of the country's "morality police" in September.
The protests since morphed into a larger anti-government uprising opposing Iran's clerical leadership, with women playing a leading role.
Germany has repeatedly lodged protests against the Iranian authorities' brutal crackdown against demonstrators, with Foreign Minister Annalena Baerbock saying the execution of the protesters will have consequences.
