No one was injured in the incident.
As many as 16 people were rescued after the blaze erupted on the 19th floor of the 26-storeyed Jolley Maker building in Cuffe Parade area at about 3.45 AM, they said.
At least nine fire tenders, two water tankers and two ambulances were rushed to the spot.
During the rescue operation, the people trapped on the 19th floor and above were rescued and the flames were doused by 9.15 AM, officials said.
The situation is under control and cooling operations are underway, they added.
Fire brigade officials suspect that short-circuit could have triggered the blaze.