The vessel, operating under a Mongolian flag, capsized 5-6 km (3-4 miles) off the harbour area after it had loaded iron ore at Paradip port, the port's Deputy Chairman Biplav Kumar said.
"Of the total 27 crew members, 26 have been rescued," he said, adding the accident had not disrupted shipping traffic. Kumar did not say why the ship sank. Rescuers are currently trying to find the missing crew member.