The constable, who has been identified as Insaaf Khan, was posted at Jamia Nagar police station in south Delhi and allegedly raped the eighth standard student.
Khan has been placed under suspension and was arrested after the medical examination of the victim confirmed rape.
A senior district officer said Khan, who hails from Bihar, has been sent to judicial custody.
The girl had alleged that the constable raped her at his friend's flat in Pul Prahladpur on Friday. Khan had allegedly befriended the girl in the local market some days back.
The girl's family had told police that the constable had told the victim not to tell anyone about the incident.
However, the girl told her parents after which they lodged a complaint.