Two bodies have been recovered so far.
Rescuers say that the salvage operation is being disrupted due to strong currents.
Louhajang Police Station OC Tofazzal Hossain told bdnews24.com that the vessel, Pinak-6, went down around 11.30am while it was heading towards Munshiganj's Mawa from Madaripur's Kewrakandi.
Two bodies were recovered until 1.30pm, he said.
Munshiganj's Deputy Commissioner (DC) Md Saiful Islam said that 44 passengers were rescued until 12.15pm. Rescuers are searching for survivors around the area where the vessel sank.
Quoting Mawa port's Launch Owners' Association President Iqbal Hossain, OC Hossain said that over 200 passengers were on board the vessel.
A survivor of the sunken ferry, however, told reporters at the Mawa landing point that the vessel was carrying over 300 people.
He added that he saw nearby speed-boats rescuing 50 to 60 passengers of the sinking vessel until 1.30pm.
Rescuers comprising of police, fire service, coast guard, RAB, Army and Navy personnel have rushed to the spot at the Louhajang Turning Point in the river, accident site.
But a strong current was hampering their operation.
Locals had immediately started rescue work with trawlers and speedboats. Later, the coast guard and fire service joined them.
Shipping Minister Shajahan Khan has rushed to spot.
Munshiganj DC Md Saiful Islam said that BIWTA's rescue vessels MV Rustam and MV Hamza were heading to Munshiganj from Naryanganj and Barisal respectively.
On May 15, a passenger vessel sank at Munshiganj's Doulatpur area in river Meghna, which claimed 58 lives.