Dozens more have been reported missing in the Chittagong Hills, following some of the heaviest rains in recent years.
Rescue operations are being hampered by bad weather and officials told the BBC they feared the death toll would rise.
Telecommunication links and electricity have been cut off in some areas.
"We have not been able to reach many of the affected places," Reaz Ahmed, head of the Department of Disaster Management, told AFP.
"Once the rains are over, we'll get a full picture of the damage and get the recovery work in full swing," he said.
Bangladesh has been hit by heavy seasonal rains in recent days
Traffic in the capital Dhaka and Chittagong, Bangladesh's major port city, has also been disrupted by the torrential rains.
Last month, at least eight people were killed and thousands of homes were destroyed after Cyclone Mora smashed into Bangladesh's southeast. Up to one million people were evacuated.
Landslides caused by monsoons often occur in the southern hills in Bangladesh. In 2007, about 130 people were killed by a landslide in Chittagong.