Rescue workers were digging through the rubble on Friday.
The building was in an area of Nairobi known as South C, according to the Kenya Red Cross, which said in a statement that a multi-agency response team was at the scene "managing the situation".
Geoffrey Ruku, the cabinet secretary in charge of public service, told reporters that four people were believed trapped.
Safia Ali Aden, the sister of one of those trapped, told reporters at the scene that her brother made a phone call "while under there".
"We are asking the government to be speedy in the rescue so we can find my brother alive," she said.
There was no immediate comment from authorities on the likely cause of the collapse.
Building collapses are common in Nairobi, where housing is in high demand and unscrupulous developers often bypass regulations or simply violate building codes.
After eight buildings collapsed and killed 15 people in Kenya in 2015, the presidency ordered an audit of buildings across the country to see if they were up to code.
The National Construction Authority declared that 58 per cent of the buildings in Nairobi were unfit for habitation.
16°C