Millions of others have been stranded as rescue workers struggle to reach those affected.
At least 59 people are known to have died in lightning strikes and landslides triggered by severe monsoon storms in India and Bangladesh.
Millions of people have been stranded while emergency workers have struggled to reach those affected.
Forecasters are warning that the flooding is expected to get worse over the next few days.
Bangladesh government officials have described the recent flooding as the country’s worst since 2004.
Unrelenting rains over the last week have inundated vast swathes of the country’s north-east region, exacerbated by runoff from heavy downpours across mountains in neighbouring India.
Schools have been converted into makeshift shelters and troops have been deployed to evacuate households cut off from neighbouring communities as a result of rising waters.
“The whole village went under water by early Friday and we all got stranded,” Lokman, whose family lives in Companiganj village, told AFP news agency.
“After waiting a whole day on the roof of our home, a neighbour rescued us with a makeshift boat. My mother said she has never seen such floods in her entire life,” the 23-year-old added.
Another woman rescued from the floods said she had been unable to eat for two days.
“The water rose so quickly we couldn’t bring any of our things,” she told the news agency. “And how can you cook anything when everything is underwater?”
In Assam state in neighbouring India, more than 1.8 million people have been affected by floods after five days of incessant downpours.
Assam chief minister Himanta Biswa Sarma told reporters he had instructed district officials to provide “all necessary help and relief” to those caught in the flooding.
This week’s rains come as Bangladesh’s Sylhet region was still recovering from its worst floods in nearly two decades in late May, when at least 10 people were killed and four million others were affected.
Syed Rafiqul Haque, a former lawmaker, said Bangladesh was at risk of a humanitarian crisis.
“Almost the entire Sylhet-Sunamganj belt is under water and millions of people are stranded,” he was quoted by Reuters as saying.
Some 3.1 million people were displaced in the region, officials said, with 200,000 of them now being housed in makeshift shelters on higher ground.
Seasonal monsoon rains represent a lifeline for farmers across South Asia, but typically cause deaths and destruction to property every year. Bangladesh and India have both experienced increasing extreme weather in recent years.
Environmentalists – while not ascribing single weather events to climate change – do warn it could lead to more disasters, especially in countries that are low-lying and densely populated.