Witnesses told police he slipped and fell to the ground floor.
He was rushed to Mama Lucy Hospital where he was pronounced dead while being attended to.
Police were called to the scene and processed it.
The body was moved to the mortuary pending further processing, Nairobi police boss Adamson Bungei said.
He said the fall was accidental but police are handling the matter.
In the same area, police said they recovered the body of an unknown man on the roadside.
The body had no visible injuries and it was established he works at the dumpsite area.
The cause of the death of the man is yet to be established. The body was moved to the mortuary pending identification and autopsy.
Elsewhere in Mukuru slums, police said they are investigating the discovery of a male body in a house.
The body was identified as that of James Muthama. Police say they are yet to establish the cause of the death and that an autopsy is planned on the body.
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