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.
After the fire was extinguished, a rescue operation continued. "It will take time given the vastness of the area," Sunil Choudhary, deputy chief fire officer, was quoted as saying by Times of India.
Most of the bodies were reportedly found on the second.
Local official Jogi Ram Jain, said preliminary reports suggested a short circuit had caused the fire and that the building did not have proper fire safety certification.
"We have initiated an inquiry and if any municipal officials are found to be at fault, strict action will be taken," he was quoted as saying by the Hindustan Times.