The storm has driven strong winds and rain over the country since Friday, and could last a few more days, the meteorological department said.
Two people were killed when a tree uprooted by the wind fell on them at a village in Chandpur district 170 km (106 miles) southeast of the capital Dhaka on Sunday.
The meteorological department said at 0600 GMT on Sunday, the storm was about 635 km (400 miles) southwest of Chittagong.
It was expected to intensify and move in a north or northeasterly direction to make landfall between Barishal and Khulna by Monday afternoon.
The storm was likely to sweep the coasts with a tidal surge of up to two metres above normal levels, the met office said.
Storms batter the poor south Asian country every year. Cyclone Sidr ravaged the coasts last November, killing nearly 3,500 people and displacing some two million.
A cyclone in 1991 killed nearly 140,000 Bangladeshis and another in 1970 killed half a million.
(Reporting by Nizam Ahmed; editing by Andrew Roche) (email@example.com; +880-2-8330123; Reuters Messaging: firstname.lastname@example.org))
- Reuters - Thomson Reuters Foundation
- For more humanitarian news and analysis, please visit https://www.trust.org/alertnet