Babak Zanjani, the chairman of Sorinet Group, was arrested on Monday afternoon, Mehr news agency quoted judiciary spokesman Gholamhossein Mohseni-Ejei as saying.
Iran's state news agency IRNA cited an unnamed source as saying Zanjani had been transferred to Evin prison in Tehran.
No comment was immediately available from Sorinet. Zanjani has denied any wrongdoing.
Iran's Press TV said Zanjani had been arrested on corruption charges and quoted the head of the Supreme Audit Court, Amin-Hossein Rahimi, as saying the National Iranian Oil Company had tasked him with exporting oil worth $3 billion.
"The problem is that they were supposed to get collateral from him by law and this was not done. This is a violation," Press TV quoted Rahimi as saying.
The US Treasury Department slapped financial penalties on Zanjani and a network of companies in April, accusing them of trying to evade sanctions over the nuclear program by moving billions of dollars on behalf of the Iranian government.
Zanjani was already a target of sanctions from the European Union, which described him a year ago as "a key facilitator for Iranian oil deals".
After the US penalties were announced in April, Zanjani told Reuters the publicity had helped his business, which has up to 65 companies operating in cosmetics, food, oil and aviation.
On Saturday President Hassan Rouhani asked his government to be vigilant in identifying businessmen who had profiteered from sanctions.
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