The fire broke out at 05 in the morning in a factory building where about 60-70 workers were sleeping, Hindustan Times reports.
The emergency services chief Atul Garg says at least 56 people were taken to hospitals, all unconscious because of the smoke. Over 40 of them have since passed away.
"We have saved at least 50 people," says New Delhi's Deputy Fire Chief Sunil Choudhary.
The factory is located in the Anaj Mandi area of north Delhi and consists of five floors.
The Times of India states that it has been difficult to obtain rescue vehicles in the narrow streets.