Two women who were helping with the building's construction told the Nation that they noticed cracks on the ground floor walls this morning.
A construction worker who spoke to the Nation said City Hall officers were arrived at the site on Tuesday morning for inspection. The officers are said to have advised workers to leave the construction site immediately.
However, the building's supervisor reportedly asked the workers to ignore the warning and proceed with construction.
Those injured have been taken to St Francis Hospital in Kasarani.
Ronald Karauri, the MP for Kasarani, arrived on site following news of the building collapse.