Rescue teams worked overnight to clear the burnt out four-storey building near a railway station in the western suburbs.
More than 75 people were in the building when the fire broke out on Friday evening. Some jumped from windows to save themselves, according to eyewitnesses, and firefighters broke the glass and rescued people with ropes.
Authorities said fire started in an office on the first floor and spread rapidly. Two owners of the company were arrested as part of probe to identify suspected safety violations.
Offering condolences, Prime Minister Narendra Modi promised 200,000 rupees ($2,580) in compensation for the victims' next-of-kin.
(Reporting by Anushree Fadnavis; Writing by Nupur Anand; Editing by Simon Cameron-Moore)