"The six were sleeping when the wall of their mud-built house collapsed in torrential rains early Saturday morning near the northeastern town of Habiganj," local police chief Mohammad Shajahan said.
Police control rooms said heavy rains also triggered flash floods in some north and northeastern districts as rivers burst their banks, stranding tens of thousands who live in low-lying areas.
Bangladesh suffers annual floods, with at least a fifth of the country submerged each year. The country is criss-crossed by a network of 230 rivers, most of them tributaries of the Ganges and Brahmaputra.
The government's Flood Forecasting and Warning Center said 46 out of 73 rivers it monitors daily had recorded a sharp rise in water levels, inundating a vast swathe of land in the northern region.
The situation is likely to deteriorate in the next few days, as heavy rains are expected in the region.
In 2007, flooding killed more than 1,000 people and some 40 percent of the country was under water, forcing millions to flee their homes.