The Kenya Red Cross and witnesses said four of those rescued had been rushed to the Kenyatta National Hospital for treatment.
“The building collapsed at about 2am and it took time for rescuers to get here,” a witness at the scene said as efforts to reach others trapped gathered pace at the break of dawn.
By about 10am, rescuers were in contact with four people trapped under the rubble.
Nairobi Deputy Governor Jonathan Mueke led officials in monitoring the rescue effort that was undertaken by personnel from the Nairobi County Fire Brigade, Kenya Red Cross and the National Youth Service.