Local police chief Mohammad Shahabuddin Khan said about 35 people were rescued after the ferry sank on the Meghna River after colliding with a cargo boat early in the morning. Divers have since recovered 30 bodies from inside the sunken ferry, he said.
He said the dead included a young woman found cradling her baby's lifeless body.
"The death toll is likely to rise as more bodies are feared trapped inside," Khan said. "We will get a better picture of the casualties once the sunken ferry is pulled out of the water."
Hundreds of anxious people, many of them weeping, gathered near the scene of the accident to look for their loved ones.
The MV Shariatpur-1 was traveling to the capital, Dhaka, from neighboring Shariatpur district to the southwest. The accident site is in Munshiganj district, about 20 miles (32 kilometers) south of Dhaka.
Dulal Dewan, a survivor, described a scene of chaos as the ferry collided with the other ship.
"I was awakened with a big jolt," said the businessman, who was asleep on the top deck. "I jumped into the river in darkness as the ferry started going down."
"In minutes there were screams all around," he said. "People were shouting for help."
Dewan said he was rescued by a nearby boat, but eight other family members traveling with him were still unaccounted for.
Estimates varied as to how many people were on board the ferry.
Khan put the number at close to 200, while Dewan told reporters that about 300 people were on board when the double-deck ferry sank.
It is difficult to get a reliable estimate as ferry operators rarely keep a list of passengers. Most passengers buy tickets once on board.
Abdul Gani Akhand, 75, was among the survivors.
"I was sleeping and I really don't know how I survived," he said, shivering as a rescue worker ferried him to a hospital.
Azizul Alam, the area's government administrator, said an investigation has been ordered into the cause of the accident.
Alam said rescuers located the ferry in water about 70 feet (21 meters) deep. He said a rescue vessel was trying to pull the sunken boat close to the shore.