The residents of the building had already been evacuated after the Brihanmumbai Municipal Corporation declared the structure as "dangerous".
The deceased was identified as Chandrakant Singhvi.
Five fire engines were rushed to the spot, they added.
Meanwhile, heavy rains lashed the metropolis since Tuesday night causing disruption in rail traffic while the flight operations remained normal. There was water-logging in some areas in the city and suburbs.
The movement of vehicles on roads was disrupted and traffic snarls were witnessed at some places. "Trains on the central line are running about 20-25 minutes late," a central eailway spokesperson said.
However, the services on Western line was normal.
"All flight operations are normal and there is no disruption or any delay," Chhattrapati Shivaji International Airport spokesperson said.
