Mohammad Jahangir Alam, the officer in charge of Nikli police station in Kishoreganj district, said the ferry was caught in a storm on Monday and capsized in the Ghorautura river, nearly 180km from Dhaka.
"We have recovered 40 bodies from inside the ferry and efforts to recover others continue," Jahangir said on Tuesday.
He said that only about 25 of of nearly 150 passengers on board the vessel managed to swim to shore.
Ferry accidents occur frequently in Bangladesh and hundreds of people die every year.
Poor enforcement of safety laws means boats are often badly serviced and often packed beyond capacity.