This incident happened in the early hours of Friday in a river near Jhalokathi, 250 kilometers (160 miles) south of Dhaka, NDTV (New Delhi Television) reported.
"We have recovered 37 bodies. The death toll may rise. Most died from the fire and a few by drowning after many people jumped into the river," local police chief Moinul Islam said.
The blaze was believed to have originated in the engine room and ripped through the ferry, Islam said.
Despite having an official capacity of 310 the vessel was carrying at least 500 people, many of who were returning home from the capital.
"We have sent some 100 people with burn injuries to hospitals in Barisal," he said. Witnesses said the fire originated at around 3:00 am (2100 GMT) and quickly spread.
"A lot of people ran for safety as the fire spread. A lot of people could not get out of their cabins where they were sleeping.
Many jumped into the river," said a survivor at Barisal Medical College Hospital. According to the TV network, investigations have been started to determine the cause of the incident.