The disaster occurred in the morning near the city of Jhalokati, about 250 kilometres south of the capital Dhaka.
“The three-storey Obhijan 10 has caught fire in the middle of the river. We recovered 36 bodies. The death toll could rise,” said Moinul Islam, the spokesman for the local police.
“Most of them died in flames, but a few people drowned after jumping into the river,” the statement said. More than 100 people have been taken to hospital with burns.
The total number of people on board ranges from 500 to 1,000.