The family went back to bed and "just afterwards the wall collapsed".
Located on the Congo River, Kinshasa has seen a huge population influx in recent years.
Many dwellings are shanty houses built on flood-prone slopes and the city suffers from inadequate drainage and sewerage.
A major landslide occurred in the hilly district of Mont-Ngafula, smothering National Highway 1, a key supply route linking the capital with Matadi, a port further down the Congo River and a crucial outlet to the Atlantic Ocean.
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.
The highway should be reopened to small vehicles within the next day, but it could take "three or four days" for trucks, the prime minister said.
The streets in the up-market government district of Gombe, which houses ministries and embassies, were also inundated.
In November 2019, around 40 people in Kinshasa died in floods and landslides.
Mont-Ngafula was one of the worst-hit areas, but a local resident said the flooding this time was even worse.
"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."
Another man, who gave his name as Freddy, said everything in his home was under water -- "shoes, food stocks, clothes. Everything is lost, there's nothing to be saved."
Close by, a young man was asking 500 Congolese francs (24 cents) from passers-by to carry them on his back across the submerged street.
Another man, who identified himself as a teacher, was walking barefoot in the water, holding a pair of shoes in one hand and a plastic bag containing documents in the other.
"I've got no other choice," he said. "I have to give schoolchildren an exam."