Doctors at JJ Hospital said the baby was kept in the incubator and was doing fine after the Caesarean-section delivery. But soon, the newborn developed complications and died on Sunday.
Laws in India do not allow medical terminations after 20 weeks unless there is a threat to the mother's or baby's life.
The 13-year-old's family discovered she was 27 weeks pregnant only last month. Her mother then moved the top court for permission to abort her daughter's pregnancy. A man who used to help her father run his roadside stall has been arrested on charges of raping her.
Noted gynecologist Dr Nikhil Datar was assisting the family with their petition. Last week, a bench of three judges led by Chief Justice Dipak Misra allowed the girl undergo abortion. Her lawyers called the order a "big relief". "How can a 13-year-old become a mother?" Justice Misra had observed before passing the order.
The teenager will remain in the hospital for a few days until she recovers. Doctors, however, say the pregnancy and child-birth at such an early age are going to affect her psychologically and that she needs counselling and support.
A 10-year-old rape survivor in Chandigarh gave birth to a baby girl last month after she was not allowed by the Supreme Court to abort. Another 10-year-old rape survivor in Haryana, however, was allowed to abort her nearly 21-week foetus in May.