A number of bodies have been recovered so far but police say they fear the death toll will rise.
The ferry overturned in high winds on the Meghna river in Munshiganj district, south of the capital, Dhaka.
The MV Miraj-4 capsized as it travelled from Dhaka towards Shariatpur district.
Local police chief Ferdous Ahmed told the AFP news agency that "around 20-30 people" managed to swim to safety. Officials said divers had located the sunken ferry and were attempting to recover bodies as darkness fell.
A navy ship, a salvage vessel and about a dozen speedboats were pictured helping with rescue efforts at the scene of the incident. But the width of the river, the depth of the water and the strong currents were hampering the search, officials added.
In March 2012, more than 112 people died when a ferry on the wide and fast-moving Meghna river collided with an oil tanker and sank.
The authorities have been repeatedly criticised for failing to honour their pledges to tackle lax safety standards.
