A spokeswoman for the Kenya Red Cross could not confirm local media reports that at least three people were killed.
"It is too early to speak about dead people, we don't have that information," Arnolda Shiundu told AFP.
"We don't know how many people are under the rubble, but we fear there are still several of them," she said.
"We are still searching. A crane has arrived, ambulances are here."
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They have caused flooding and landslides in many areas of the city.
"Up to now, 44 people have been rescued from the rubble," Shiundu said, without saying how many were injured.
"Our teams are on the site, where it is complete chaos," she said.
The Red Cross spokeswoman had earlier mentioned at least 15 injured.
Pictures broadcast by local media showed soldiers, policemen and civilians searching through the rubble of the collapsed buildings for survivors.
Earlier yesterday, a wall around a property collapsed due to flooding in another part of the city, killing at least three people, according to local media.
The growing middle class has triggered an explosion in demand for housing and a rise in real estate prices in the east African capital.