The victim, identified as Janki, was found dead at her father's house. Her parents, Deepak and Rajni are living separately after they filed for divorce.
Her custody was handed over to her father two months ago by a city court. Rajni and her family alleged her daughter was killed by her husband and in-laws, police said.
The incident came to light after Deepak's neighbours informed Rajni's father Rakesh that Deepak had taken Janki to Guru Teg Bahadur Hospital as she was badly injured after allegedly falling from the terrace. She was declared brought dead at the hospital.
Rakesh informed police alleging foul play in the case. In his complaint to the police, he has said the girl was called by her daughter's in-laws.
"There were multiple injury marks on Janki's chest and neck," Rakesh said.
Mansarovar Park police are investigating the case and Janki's body has been sent for post-mortem to ascertain the cause of death. Police have also questioned Deepak, Rajni, their family members and neighbours.
Deepak and Rajni had married in May 2011, but they filed for divorce after Janki's birth.