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.
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.