A local official said two passenger ferries collided head-on at around 3 am local time (21:00 GMT, Monday) on the Bhoga river about 200 km south of the capital, Dhaka, the New Kerala website reported.
Sanjoy Chakrabarty, head of the Dhumki sub-district, was also quoted as saying that neither of the ferries sank after the collision.
He said the river's strong current was hampering rescue efforts.
Ferries in Bangladesh, one of the world's most densely populated countries, often sail overloaded, especially on the eve of holidays, when people travel to be with relatives.
The collision took place before the Muslim festival Eid-ul-Fitr, which marks the end of the Islamic holy month of Ramadan.
It will be celebrated in predominantly Muslim Bangladesh on Wednesday or Thursday, depending on the sighting of the new moon.