The three were rescued nearly 19 hours after the house collapsed on Monday night.
Pius Masaai, deputy director National Disaster Management Unit, said the three were in a stable condition.
"They have been rushed to Nairobi West hospital. They are among seven people who were trapped in the rubble."
Meanwhile, four people out of the seven reported missing earlier on Tuesday, were confirmed dead.
Nairobi governor Evans Kidero appealed to the owner of the building to come forward and provide architectural plans to help rescuers.
Kidero said at least 30,000 to 40,000 buildings constructed without approval in the capital city were at risk of collapse.
Officials said the building's tenants had been asked to leave on Monday after residents reported cracks in the walls.
At least 128 people had heeded the call to leave.
A total of 49 people died in May last year when a building collapsed during a heavy, nighttime downpour in Huruma slum.
The government ordered the demolition of many other buildings after that incident.
"We hadn't got to a point where we were going to demolish it," Kidero said at the time.
-The Star| Patrick Vidija