A forecast for more torrential rain over the next few days is expected to worsen the situation.
The Disaster and Relief Ministry said on Tuesday that some 40,000 people are taking refuge in government shelters. Over 600 medical teams have been formed to treat flood victims.
Television footage showed inundated roads, broken bridges and dams, as well as villagers wading through knee-deep water.
Farmers also had to rescue cattle from the gushing waters.
“Bangladeshis are used to flooding, but the water is coming up so high and so quickly in low-lying areas that people are being forced to shelter on anything, even rafts made of banana trees,” said Liakath Ali, head of climate change programme at development agency BRAC.
The local meteorological office has forecast more rain for the central and southern regions, but the swollen Brahmaputra river is expected to recede in the next few days.
“Heavy rains in the Indian upstream region mean that the suffering is far from over. We have taken measures to cope with the situation,” said Rezwanul Rahman, the head of Bangladesh’s disaster management department.
Seasonal monsoon rains, which in May end, have triggered widespread flooding in India and neighbouring Bangladesh in recent years.
Floodwaters have started receding in India’s Assam, located north of Bangladesh, authorities said, bringing some respite to the 48,000 or so people sheltering in camps.
During the last 24 hours, six persons died due to rain and flood-related incidents, raising the death toll to 72 in the state since May.
More than two million people have been affected by the floods in Assam. The Kaziranga National Park, home to the rare one-horned rhinoceros, was also inundated.
A heavy downpour early on Tuesday in the National Capital Region of Delhi and its suburbs disrupted traffic.
Just over a week ago, unusually heavy rain in New Delhi caused a roof at the airport terminal to collapse. This week, heavy rains flooded roads and railway lines in Mumbai disrupting flights and forcing schools to close.