The report said 23 people had been on board when it went down in the Sea of Oman, south-east of Chahbahar port.
Ten of the crew were picked up by passing vessels, an official said. Eight of the crew members were South Korean, 13 Filipino and two Chilean.
Seyed Masih Momeni said the ship had been carrying iron to Iran from China.
Mr Momeni said the ship, called the Orchid Sun, had sunk because of a leak.
The identities of those rescued were not announced.
