The blaze started on the twelfth floor of Crystal Tower in Parel around 8:30 a.m. local time. It soon started spreading to upper floors, a fire official said.
"Initially we thought that we had rescued all those trapped in the fire on the upper floors, but four people eventually died of suffocation. Those injured have been admitted to a nearby hospital," a fire official added, as reported by Xinhua.
As many as 10 fire tenders were pressed into service to contain the flames, the official said, adding that the cause of the fire is yet to be ascertained.
Local TV channels aired footage of white smoke billowing out of the building and people being evacuated by fire fighters using hydraulic cranes.
A probe has been ordered into the incident, the official said.
Fires are common in highrises and factories in India because of lack of regards for basic fire safety norms and absence of fire-fighting equipment.
Some 14 people were killed in a massive fire at two rooftop pubs in Mumbai in December last year.