Major roads in the centre of Kinshasa, a city of some 15 million people, were submerged for hours, and a key supply route was cut off.
City police chief General Sylvano Kasongo, in a statement to AFP, gave a provisional toll of at least 55 dead, concentrated especially on hillside locations where there had been landslips.
Images circulating on social media showed a landslide in Mont-Ngafula district, cutting off Highway 1, a key supply route linking the capital with the Atlantic Ocean port of Matadi.
Prime Minister Jean-Michel Sama Lukonde told reporters at the scene that around 20 people there had died when "homes were swept away".
Searches are continuing for survivors, he said.
"We've never seen a flood here on this scale," said Blanchard Mvubu, who lives in the Mont-Ngafula neighbourhood of CPA Mushie.
"I was asleep and I could feel water in the house... it's a disaster -- we've lost all our possessions in the house, nothing could be saved."
He added: "People are building big houses and that blocks up the drains. The water can't move freely and that's what causes the floods."
Floods also inundated streets in the up-market government district of Gombe, which houses ministries and embassies.
Other online images showed entire neighborhoods flooded with muddy water and tarmac roads ripped apart by sinkholes.
Major roads in the center of Kinshasa, a city of some 15 million people, were submerged.
An AFP reporter saw the bodies of nine members of a family who had died after the collapse of their home in the Binza Delvaux district.
Once the site of fishing villages on the banks of the Congo river, Kinshasa has grown into one Africa's largest megacities with a population of around 15 million.
Like in other cities on the continent, poorly regulated rapid urbanization has made Kinshasa increasingly vulnerable to flash floods after intense rains, which have become more frequent due to climate change.
Many dwellings are shanty houses built on flood-prone slopes and the city suffers from inadequate drainage and sewerage. In 2019, around 40 people died in floods and landslips.
This report was prepared with data from Reuters and Agence France-Presse.