More than 70 people were in the building when the fire started and police broke windows and used ropes to rescue people.
Some 20 fire engines were used to put out the blaze near Mundka metro station in the west of India's capital.
A short circuit is thought to have started the fire.
Indian media report that two arrests have been made.
Offering his condolences over the loss of lives, Prime Minister Narendra Modi promised 200,000 rupees (£2,118; $2,580) to next-of-kin in compensation for each death.