The Southern Star 7 was carrying more than 350, 000 litres of oil when it was hit by another vessel on Tuesday.
Since then thousands of litres have spilled into the Shela River in the Sundarbans mangrove forest in Bangladesh.
The area is a wildlife sanctuary and home to two endangered dolphin species.
Local news reports said the government had closed the river to all other traffic.
That move was applauded by the United Nations Development Programme which said it was working with the government and other parties to minimise and repair the damage.