About 100 fisherman and up to 20 boats have been reported missing as rain and strong winds swept Bangladesh's coast, officials said. They said that the body of one man had already been washed ashore.
Officials have said that the storm brewing in the Bay of Bengal may trigger a tidal surge two metres high.
"The core of the storm was about 100km from Cox's Bazar at midnight on Monday and could slam the shores early on Tuesday with wind speed of 120km per hour," Deepak Chandra Nath, a meteorological official, said.
People living in coastal areas have been told to move to safer places. Merchant and fishing vessels have been advised to return to port or take shelter at nearby islands.
Flights between Dhaka and Chittagong and ferry services in coastal districts have been suspended.
Tropical storms and cyclones kill hundreds of Bangladeshis every year. One of the worst cyclones to hit the country killed 138,000 people in 1991.