The incident was reported from Rohini, Sector-2.
The deceased has been identified as Aayushi Singh, a Class IX student of Kendriya Vidyalaya.
The girl allegedly used a licensed revolver of her father Yogesh Kumar, a property dealer, to shoot herself, they said, adding that her family was out when the incident took place.
"When her parents and younger brother came back she did not respond to their calls. So they broke open the door and found Aayushi lying in a pool of blood," a senior police official said.
The girl was rushed to Ambedkar Hospital where she was declared brought dead.
No suicide note was recovered, the official said, adding that they were investigating why the girl took the extreme step.