At least 16 people have died after a cyclone slammed into Bangladesh, forcing the evacuation of about a million people from their homes, officials said.

Around 10 million people were without power in 15 coastal districts, while schools were shut across southern and southwestern regions.

Cyclones - the equivalent of hurricanes in the Atlantic or typhoons in the Pacific - are a regular occurrence, but scientists say climate change is likely making them more intense and frequent.

Cyclone Sitrang made landfall in southern Bangladesh late last night but authorities managed to get about a million people to safety before the monster weather system hit.

Fourteen people died, mostly after they were hit by falling trees, and two died after a boat sank in squally weather in the Jamuna river in the north.

People evacuated from low-lying regions such as remote islands and river banks were moved to thousands of multi-storey cyclone shelters, a Disaster Management Ministry spokesperson said.

"They spent the night in cyclone shelters. And this morning many are heading back to their homes," he said.

In some cases police had to cajole villagers who were reluctant to abandon their homes, officials said.

Trees were uprooted as far away as the capital Dhaka, hundreds of kilometres from the epicentre of the storm.

Heavy rains lashed much of the country, flooding cities such as Dhaka, Khulna and Barisal - which witnessed 324mm of rainfall yesterday.

About 33,000 Rohingya refugees from Myanmar, controversially relocated from the mainland to a storm-prone island in the Bay of Bengal, were ordered to stay indoors and there were no reports of any casualties or damage, officials said.

A feared major storm surge did not materialise, however.

On the southern island of Maheshkhali, the cyclone uprooted many trees and created panic after power and telecoms were cut.

In the neighbouring eastern Indian state of West Bengal, thousands of people were evacuated yesterday to more than 100 relief centres, officials said, but there were no reports of damage and people were returning home today.

Last year, more than a million people were evacuated along India's east coast before Cyclone Yaas battered the area with winds gusting up to 155 km/h - equivalent to a Category 2 hurricane.

Cyclone Amphan, the second "super cyclone" ever recorded over the Bay of Bengal, which hit in 2020, killed more than 100 people in Bangladesh and India, and affected millions.

In recent years, better forecasting and more effective evacuation planning have dramatically reduced the death toll from such storms. The worst recorded, in 1970, killed hundreds of thousands of people.