A spokesman for the Rangamati district administration said at least 60 people were killed in a series of landslides there alone.
Rescue operations are being hampered by bad weather.
Telecommunication links and electricity have been cut off, and some communities cannot be contacted.
“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.
In Rangamati district, a hilly area close to the Indian border, landslides buried residents’ houses.
“Some of them were sleeping in their houses on hillsides when the landslides occurred,” district police chief Sayed Tariqul Hasan told AFP.
The soldiers who died had been clearing a road in Rangamati of an earlier landslide when another one hit, a military spokesman told AFP news agency.
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 south-east. Up to a 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.