At least 23 people have been killed in Nairobi after heavy rain overnight caused severe flooding in Kenya's capital city.

Police said about 30 people had been rescued but many others drowned after being swept into rivers - some have been electrocuted.

Kenya's military has been deployed to help people trapped inside their cars as police described widespread damage to properties as well as road closures. 

Several flights bound for Nairobi Airport had to be cancelled or diverted to the coastal city of Mombasa.

"The torrential rains have led to significant flooding, unfortunately resulting in 23 fatalities so far, the destruction of property, road closures, and the displacement of residents," police said in a statement on Saturday afternoon.

Earlier, security guard John Lomayan, 34, described seeing someone he recognised in the industrial neighbourhood of Grogan who was trapped beneath a car that had been washed away when the Nairobi River burst its banks.

"I saw him being carried by the water from up there," he told Reuters news agency, gesturing up the road. 

"We didn't know where he had gone. It is only now that we see him under the car."

Key roads in the capital city, including Mombasa Road, Uhuru Highway, Kirinyaga Road, and parts of the Westlands district, have been submerged underwater.

Stalled vehicles and fast-moving floodwaters created havoc, Reuters said.

Kenyan authorities advised residents to avoid flooded streets and drainage channels while emergency responders assisted stranded motorists and pedestrians.

Earlier, the Kenya Meteorological Department warned of prolonged heavy rainfall, cautioning about urban flooding, poor visibility.

River levels are expected to rise through to 9 March.

Nairobi, along with regions such as the Central Highlands, Lake Victoria Basin, and the coastal areas, remains under heightened alert for peak rainfall in the coming days, it added.

Last year, hundreds of Kenyans were killed after heavy rains caused severe flooding and landslides across the country and neighbouring Tanzania.