Rains have also been reported from neighbouring Indian states of West Bengal and Tripura.
Senior Meteorologist Bazlur Rashid said light drizzle to moderate rains may continue across Bangladesh until Tuesday.
Squally winds and thunderstorms may also hit some areas of Khulna, Chittagong, Barisal, Sylhet, Rajshahi, Mymensingh and Rangpur divisions, he said.
The Met office reported a drop in day temperatures and night temperature may remain unchanged.
A trough of low lies over West Bengal and adjoining area of Bangladesh.
Another trough of low lies over northern part of West Bengal while Seasonal low lies over South Bay, says the met office.
In capital Dhaka, the met office has recorded 8mm rainfall during three hours from 6am on Monday.
Moderate rain was also reported in Calcutta and Agartala and other parts of West Bengal and Tripura.