The cyclone damaged hundreds of mud-and-tin houses in two impoverished southern districts, with many low-lying villages inundated by a storm surge that swelled up to seven feet (two metres) high.
Authorities took more than 500,000 people into shelters as the cyclone made landfall just after midday local time (0600 GMT), packing winds as strong as 88 kilometres (54 miles) per hour.
At least 20 people are known to have died, police said.
‘Seven people drowned at Banshkhali after the storm surge breached dykes at two places, inundating coastal villages,’ Shah Alam, a police inspector in Chittagong, told AFP.
Three people, including a mother and her daughter, drowned on Hatiya island after sea water flooded their village.
By early evening Saturday conditions appeared to be improving, paving the way for people to return to their homes, officials said.
‘Up to 20 villages were flooded (in the area),’ Hatiya police chief Anisul Haq told AFP.
‘The flood water is now receding,’ he said.
Peripheral winds and heavy downpours brought on by the impending cyclone struck coastal areas early Saturday morning, causing widespread devastation before the storm had even made landfall.
A mother and her young child were killed after rains triggered a landslide which buried their hillside home at Sitakundu in Chittagong District, a police inspector said.
Others died on Bhola island and in Cox's Bazar, Laxmipur and Patuakhali, officials said.
‘So far we have moved more than 500,000 people to cyclone shelters,’ Reaz Ahmed, the head of Bangladesh's Disaster Management Department, told AFP.
‘Many have started to return to their homes as the wind speed has abated,’ he added.
Disaster authorities shut down sea and river ports on Saturday and ordered fishing trawlers and other boats not to go out on the water.
The government's meteorological department has warned of the risk of further landslides in the country's southeastern hill districts.
Officials told AFP Friday night that they were prepared to move more than two million people to nearly 4,000 cyclone shelters in the country's south.
It comes as a week of extreme weather wreaked havoc across South Asia with Sri Lanka battered by the heaviest rains in a quarter of a century, triggering severe floods and landslides.
Earlier this month lightning strikes killed an unprecedented 59 people in Bangladesh in three days as tropical thunderstorms hit the country before the annual monsoon, which runs from June to September.
Most of the victims were farmers struck while working in their rice paddy fields.