"The three-storey Obhijan 10 caught fire mid-river. We have recovered 32 bodies. The death toll may rise. Most died from the fire and a few by drowning after they jumped into the river," local police chief Moinul Islam told AFP.
The incident took place early in the morning near the southern rural town of Jhakakathi, 250 kilometres (160 miles) south of the capital Dhaka in Bangladesh.
The accident was the latest in a string of similar incidents in the low-lying delta country criss-crossed by rivers, the report said.
Experts in the South Asian country of 170 million people blame poor maintenance, lax safety standards at shipyards and overcrowding.