"We are already at around fifty deaths and that is not yet final," police chief Sylvano Kasongo told Reuters news agency on Tuesday.
In the Binza Delvaux district of the city, an AFP news agency reporter witnessed nine people killed when their home collapsed.
Major roads in the center of Kinshasa, a city of some 15 million people, were also submerged.
Floods also inundated streets in the up-market government district of Gombe, which houses ministries and embassies.
Images also 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.
Other images shared online, which could not be immediately verified, showed entire neighborhoods flooded with muddy water and tarmac roads ripped apart by sinkholes, TRT World reported.
Located on the Congo River, Kinshasa has seen a huge population influx in recent years.
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 the climate crisis.
Many dwellings are shanty houses built on flood-prone slopes and the city suffers from inadequate drainage and sewerage.
MA/PR