The landslides hit hilly districts in the southeast, killing 10 people in one village, eight in another and seven in a third, said police official Rafiq Ullah.
The death toll could rise further as rescuers search for bodies and dozens of people are still missing, he said.
The dead include four soldiers who had joined the rescue operation, said a spokesperson for the control room of the Disaster Management and Relief Ministry in Dhaka.
The latest fatalities came weeks after Cyclone Mora lashed Bangladesh 's southeast, killing at least seven people and damaging tens of thousands of homes.
In 2007, about 130 people were killed in a landslide in Chittagong in the southeast.