"The death toll is provisional, but so far there are around thirty dead," Patricien Gongo Abakazi told Reuters.
The Ndjili River, which runs through part of the city of around 17 million, overflowed its banks on Friday night, blocking the main national road and leaving drivers stranded since Saturday evening.
"On the way home from the airport last night to welcome a friend, we spent the night in the car because there was no safe place to park," said Patricia Mikonga, a Kinshasa resident.
Several neighbourhoods were left without power.
Kerene Yala, a resident of Makala district, said the main problem in the area was the water supply cutoff.
Kinshasa Governor Daniel Bumba Lubaki said the water infrastructure had been affected but that supply would be reinstated within two or three days.
In a televised speech, he blamed illegal housing for some of the deaths and threatened to evict people from unplanned settlements.
Hydrologist Dr Raphael Tshimanga Muamba said the river had been affected by human activity over time.
"These are anthropogenic actions where rivers are degraded; their dimensions no longer represent their initial capacity to contain floods," he told Reuters.
The flooding comes at a vulnerable moment for the Central African nation. Rwanda-backed M23 rebels have intensified an offensive in the turbulent east of the country since the start of the year, with more than 7000 people killed in the fighting in the first two months of the year.
