Police said preliminary investigations revealed that the woman, and her second husband, identified as Lalitha M and Y Prakash respectively, wanted to get rid of the child.
The couple, both 25 years of age, have been working as cook and watchman at a hostel in SR Nagar, police added.
"The girl is from Lalitha's first marriage. She seems to have left or divorced her first husband and married Prakash. The girl was found with burn injuries on her body after her mother allegedly made her sit on a frying pan. The burn injuries seem to be from around 4-5 days ago," SR Nagar police station inspector Md Waheeduddin said.
"During verification it was revealed that the child was being "tortured" by the couple who wanted to get rid of her," city-based child rights NGO Balala Hakkula Sangham honorary president Achyuta Rao said.
Based on a complaint lodged by an official of the Child Welfare Department, a case was registered under IPC section 324 (voluntarily causing hurt by dangerous weapons or means) and relevant provisions of the Juvenile Justice (Care and Protection of Children)Act against the couple leading to their arrest, inspector Waheeduddin said.