Bangladesh is relocating two million people from its coastal areas before cyclone Roanu's likely landfall on Saturday evening.
Officials said on Friday authorities in neighbouring India and Myanmar are also on edge.
The cyclonic storm brought about heavy rains this week in Sri Lanka, triggering two landslides that were feared to have killed about 150 people and forced more than 223,000 from their homes.
"Low-lying areas of (Bangladesh's) coastal districts ... are likely to be inundated by storm surge of 4-5 feet height above normal astronomical tide," its weather office said on its website.
India Meteorological Department said on Friday evening the storm was likely to move along the country's east coast and intensify into a "severe" cyclone in the next 24 hours, before crossing the south Bangladesh coast on May 21 as a cyclonic storm with lesser intensity.
Bangladesh's disaster ministry secretary Mohammad Shah Kamal told reporters the country had already taken "all sorts of steps" to minimise any losses, including moving people away from the eye of the storm. India's Andhra Pradesh state has also moved some people from low-lying areas.
Bangladesh, a poor South Asian country, has been one of the worst victims of nature's fury in recent years. More than 3000 people were killed by Cyclone Sidr in 2007 and about 200 lives were lost to Cyclone Aila in 2009.