Bujumbura Mayor Freddy Mbonimpa on Sunday evening said another 30 people were injured and dozens of homes were damaged or destroyed in the landslides earlier in the day in the north of the capital.
One 50-year-old survivor who gave her name only as Angele said she lost her four children and her husband when their house was destroyed. She said she was spared because she had been away at work.
Other residents told The Associated Press they feared the toll would be higher as searches continued for missing people.
Security Minister Alain Guillaume Bunyoni during a visit to affected neighborhoods said authorities would install provisional shelters for those who lost their homes.
Heavy rains in recent weeks across East Africa have killed scores of people. Earlier this month, authorities in Burundi said at least 28 people died in landslides.