All residents have been evacuated. Around 10 to 12 people have been taken to a hospital. Earlier, there were reports that at least 10 people on higher floors were trapped inside.
The fire allegedly began in an office on the ninth floor of the Everest Tower in Tardeo, South Mumbai.
It is a 10-floor building and earlier this evening, people were seen standing at the windows of their flats waiting for firemen to help them.
Electricity was disconnected in the building when the fire was spotted; so lifts are not working.
Eight fire engines and eight water tankers were initially called in to fight the flames.
The ground floor of the building, which is close to the famous Haji Ali shrine, has shops.
Film maker Shyam Benegal, ad man Prahlad Kakkar and former cricketer Sunil Gavaskar have offices in the building.