Landslides struck the beach town of Cox’s Bazar and Ramu Upazila, Abdul Malek, a spokesman for Bangladesh Fire Service and Civil Defence, told bdnews24.com.
A woman was killed in the coastal district's Pekua Upazila after a wall in her home collapsed.
The dead have been identified as 7-year-old Jihan and his 5-year-old sister Saima, Mohammad Shahed, 18, Saddam Hossain, 28 and Anwara Begum, 60.
The two children were killed in a landslide in Ramu Upazila.
Shahed was killed and three others, including Saddam Hossain, were injured in a landslide in the lighthouse area of the Cox’s Bazar town.
The injured were taken to Cox’s Bazar hospital for treatment, where Saddam later succumbed to his injuries.
Saddam’s brother Arfat Hossain, 30, and local resident Delwar Hossain, 25, are still undergoing treatment.
Sixty-year-old Anwara Begum died on the spot, said local UP Chairman Zahedul Islam Chowdhury.
He said they suspect heavy rains caused the wall of the house, near a hill, to collapse.
Intermittent heavy rains began from Monday afternoon and continued steadily overnight, said Cox’s Bazar Assistant Meteorologist AKM Nazmul Haq.
In the 24 hours before 6am on Tuesday, 208 millimetre of rains have been recorded in the coastal district, he added.
Forecasts of more rain on Tuesday and Wednesday raised fears of more landslides.
More than 150 people died last month in landslides triggered by heavy rains in five southeastern Bangladesh districts, including Cox's Bazar.