The blaze erupted just after midnight at a building in the popular Kamala Mills restaurant and shopping compound. It engulfed the structure within 30 minutes, local media reported.
More people have been injured in the blaze with several being treated in hospital.
The fire started at the 1 Above rooftop restaurant, media reported.
According to the Times of India, many of the guests tried to seek shelter in the bathroom and got trapped there. The paper also cites a hospital doctor saying that all the deaths were due to suffocation.
TV and social media footage showed fire fighters and rescue teams at the scene with the top of the building consumed by flames and plumes of smoke.
Most of the casualties were women attending a party. A 28-year-old woman who was celebrating her birthday died in the fire, according to her grandfather who spoke to the Reuters news agency.
Indian President Ram Nath Kovind tweeted his condolences to the families of the victims.
Kamala Mills is a refurbished industrial compound and houses several upscale restaurants, bars, offices and hotels.
It is also home to several media outlets with a number of national news channels affected by the fire, including Times Now, Mirror Now and ET Now.
Police have reportedly launched an investigation.