Residents were evacuated to safety when the building developed cracks and then collapsed, police said.
"There are people reported missing in the tragedy," a senior police officer said.
A total of 121 people are accounted for, said Pius Masai, deputy head of communications at the National Disaster Management Unit.
"It is believed that some people may have been trapped. Rescue efforts are ongoing," he said in a statement.
He "appealed to anyone with cutters, drillers and any other extrication equipment" to support search and rescue efforts.
Building collapses are a recurrent problem in Kenya, where construction standards are weakened by chronic corruption.
In April 2016, 49 people were killed when a six-storey building collapsed in northeastern Nairobi after torrential rain.