Workers from the Bangladesh Inland Water Transport Authority, firefighters and soldiers were reported to be involved in the rescue operation on the River Padma, 30 kilometers (18 miles) southwest of the capital, Dhaka.
Local police chief Tofazzal Hossain said that many of the passengers had been rescued and some were thought to have been able to swim to safety. However, many others were feared trapped or drowned.
It wasn't immediately clear what caused the mishap, but the police chief said there may have been a couple of factors involved.
"We have heard that the ferry was overloaded with passengers and the river was rough," Hossain told the AFP news agency.
The number of passengers on board the vessel also wasn't clear, with estimates ranging between 170 and 250.
Ferry accidents are relatively common in Bangladesh, and overloading is often at least partially to blame.
A similar accident occurred in May, when more than 50 people died after a ferry capsized with around 200 people on board.
pfd/kms (AFP, Reuters, AP, dpa)