The girls filed an FIR against one person accusing him of misusing their photographs with objectionable captions.
They also demanded immediate arrest of the man.
"We have registered a case after girls filed an FIR and are investigating the matter," Saheed Nagar police station inspector in-charge Kishore Mund said.
Deputy Commissioner of Police Satyabrata Bhoi said the police have been looking for the accused.
Meanwhile, the objectionable page has been blocked by Facebook.