Chakravarty and his wife Radhika, natives of Prakasham district Andhra Pradesh, were booked at Bollaram in Medak district on a complaint filed by an NGO, they said.
The couple's neighbours told the NGO they had been beating and abusing their daughter, they said.
The NGO's volunteers rushed to the spot and rescued the child. They later lodged a complaint against the parents at Bollaram Police Station.
Chakravarty, who works in a private factory, and his wife have denied the charge.