The dilapidated building located near Sangharsh Nagar bus stop in Chandivali area collapsed at around 5.35 pm, said a senior official of the Disaster Management Cell of the Brihanmumbai Municipal Corporation (BMC).
Around ten persons were feared trapped in the building which was being demolished, he added.
The city had received heavy showers in the past two days.
Mumbai fire brigade chief P S Rahangdale said one person was rescued from debris and sent to a hospital. He put the number of people feared trapped inside at around five.
"Hanging portion of the remaining building is posing risk to the rescue operation," he said, adding that eight fire engines, a rescue van, a quick response vehicle, 50 workers and ward office staff have been pressed into service at the spot.