Witnesses and Police said that the structure had been built up to the fifth floor, and labours we're working on the six one, when it's collapsed on the late hours of monday afternoon along Muuru road.
Several workers managed to escape the rubbles soon after the 3pm incident.
Those who escaped said that they have sustained some injuries.
It is not clear the exact number of people who are trapped in the rubbles.
The building was meant to be a residence.
Kiambu police boss Ali Nuno said that, the rescue operations is ongoing and no death have been reported so far.
Nairobi and Kiambu are among the areas that are frequently experiencing collapsed buildings as many of the building have more than 10 floors.
There have been concerns of structures being constructed without proper supervision.
This comes after nine people died last week at hurlingham region in Nairobi after crane crumbled on a construction site.
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