Reuters photographers on the scene -- in the eastern Nairobi suburb known as Pipeline -- saw a pile of broken concrete blocks and bent metal. An excavator was moving rubble.
The incident occurred on Monday night.
Officials said the building's occupants had been asked to leave once it developed cracks.
"Basically this was a disaster to come. An evacuation was sounded. People evacuated but we might have some people who might have been left behind," Pius Masai, deputy director of the National Disaster Management Unit, told Reuters at the site of the collapse.
Japheth Koome, Nairobi County police commander, said a specialized team from the Kenya Defense Forces had been called in to help with the rescue operations.
Kenya has seen similar tragedies in the past. A total of 49 people died in the middle of last year when another building collapsed during a heavy, nighttime downpour in a poor neighborhood.
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