Pinki, a class XII student in government school at RK Puram Sector 5, was killed by the youth at her home in Budh Vihar area of Munirka, police said.
The youth, later identified as Subhash, entered the house, closed the girl's room and allegedly pumped bullets into her chest, a senior police official said.
Pinki was rushed to Safdarjung Hospital where she was declared brought dead.
Subhash was arrested tonight.
"Her aunt was present in the house when the incident took place. After shooting her the boy fled from the scene," the official said.
Pritam is a plumber while the girl's mother works as a domestic help. Pinki was their only child and was waiting for her Class XII results.