The fire broke out after the ship was hit by a missile, the seafarers' union in India told CBS News.
The Palau-flagged ship Marivex caught fire earlier on Monday. All evacuees escaped without injury, the AFP news agency reports.
The ship, under a previous name - Arihant - is subject to sanctions by the US due to alleged links to Iran, according to CBS, but it is unclear who fired on the ship.
The US maintains a blockade of Iranian ports and, during the ongoing ceasefire with Iran, has both shelled and redirected merchant ships in the area.
