The girl, who cannot be named for legal reasons, was raped several times allegedly by an uncle who has since been arrested.
Last month her parents asked the country's top court to allow her to have a late-term abortion but the request was turned down.
Indian law does not allow medical terminations after 20 weeks unless there is a threat to either the life of the mother or her child.
"She gave birth through C-section today (Thursday). Both the girl and her baby are doing fine," doctor Dasari Harish told AFP by phone from the northern Indian city of Chandigarh.
"The surgery was uneventful. There were no complications whatsoever. The baby weighed 2.2 kilos (4.8 pounds) and is in the neonatal ICU for now."
The Press Trust of India news agency said the girl was unaware that she had delivered a child and the parents had decided to put the baby up for adoption.
Her parents have told her that she had a stone in her stomach and had undergone surgery to remove it, PTI said.
India has a grim record of sexual assaults on minors with 20,000 cases of rape or sexual assaults reported in 2015, according to government data.
