The woman's daughter and son are in a stable condition after being pulled from the debris in a poor neighbourhood near Nairobi's international airport, southeast of the Kenyan capital.
"Unfortunately one female adult, believed to be the mother of the rescued children, succumbed to the injuries while undergoing treatment at the hospital," said Pius Masai, National Disaster Management Unit spokesman, who is coordinating the search and rescue mission after Monday night's tragedy.
The incident has renewed criticism over unregulated construction in the city of more than three million people.
Police and local residents said the authorities were alerted on Monday after cracks appeared in the building, sparking an emergency evacuation before it collapsed two hours later.
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Officials said they evacuated most residents, but at least two people are still feared to be missing, according to the Red Cross.
In all, 128 tenants have been accounted for, but it was not immediately clear how many people lived in the building.
Several buildings have collapsed in recent years in Nairobi and other Kenyan cities, where a property boom has seen buildings shoot up at speed, often with little regard for regulations.
In April 2016, 49 people died when a six-storey building collapsed in a poor neighbourhood northeast of the capital after days of heavy rain caused floods and landslides.
The building, constructed two years earlier, had been slated for demolition after being declared structurally unsound.