The region along the Bangladesh-Myanmar border where nearly one million Rohingya refugees from Myanmar are in camps has been battered by torrential rain since Monday.
"The floods have stranded some 306,000 people in Cox's Bazar district. At least 70 villages have been submerged by floods," Mamunur Rashid, the district administrator, told AFP.
"At least 20 people have died in floods and landslides including six Rohingya refugees," he added.
About 36,000 people have been moved into schools and cyclone shelters, officials said.
"Many homes are waterlogged. Thousands of people have not been able to get out for the last three days. The roads are all blocked," Tipu Sultan, a councillor in remote Jhilwanja Union, told AFP by telephone.
Earlier this week Bangladesh evacuated 10,000 Rohingya from around refugee camps in Cox's Bazar because of the storms.
Aid workers said a coronavirus lockdown in the camps, following a major spike in cases, has affected rescue work as access is restricted.