The accused had created eight fake IDs of girls using proxy servers, a senior police officer said.
"This was one of the most difficult cases because the accounts were created using proxy servers. Finally, we zeroed in on the girl," said Karthik Kashyap, Superintendent of Police (Cyber Crime).
The device used to commit the offence is being recovered from the accused.
"The accused was in the habit of creating fake profiles. She is a friend of those whose accounts are created on facebook," Kashyap said, adding that the motive behind the act is being investigated.