According to Sufia Begum, a fire brigade official in Dhaka, most of the bodies were found inside the hull of the wooden ferry, named MV Saurav.
Local residents have joined police and fire brigade divers in the rescue operation.
The ferry had been travelling from Dhaka to the nearby town of Taltala.
This was the first major ferry disaster in Bangladesh since May 2005, when 150 people were killed after a ferry with 200 passengers went down in a river during a storm.
Ferry accidents, blamed on lax rules and unsafe practices, are common in the country.