Fire broke out at an apartment complex that is located next to Ridgeways Mall, along Kiambu Road, on Sunday morning.
According to a report by The Star, one person died while several others sustained serious burns.
A senior police officer told the publication that the victims were rushed to a nearby hospital.
Residents alerted firefighters who responded swiftly and extinguished the fire in minutes.
They had to bring down doors while trying to rescue those who were asleep inside the flat.
The cause of the fire was not immediately established.
Kenya Red Cross personnel and Nairobi County Fire Brigade are currently conducting a search and rescue operation.
The flat has since been cordoned off.
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