Police in southern Hyderabad city told BBC Hindi they want to know if Aradhana Samdariya was forced to fast.
Her parents have insisted she voluntarily fasted as prescribed in Jainism, one of the world's most ancient religions. The case has sparked a debate about the practice of religious fasting in India.
Reports said Aradhana lived for 68 days on boiled water. Two days after she called off her fast last week, she was dead.
Experts believe it is possible for the human body to survive without food for up to two months.
A police spokesperson said a case had been registered against the parents after a child rights organisation filed a complaint.
"The parents - Laxmi Chand and Manshi Samdariya - have been booked under culpable homicide [causing death by negligence] and Juvenile Justice Act [cruelty against minors]," the spokesperson said.
The parents, wealthy jewellers based in Hyderabad, have denied that they forced their daughter to fast.
"She asked permission for upvaas [fast that involves renouncing food]. We asked her to stop after 51 days but she would not give up. Her fast was voluntary. No one forced her," Mr Samdariya said.
But social activists have rejected the family's claim.
"The entire nation should be ashamed that such a practice still exists. Her father's guru advised the family that if she fasted for 68 days, his business would be profitable," activist Achyut Rao told BBC Hindi.
"The girl was made to drink only water from sunrise to sunset. There was no salt or lemon or anything else."