The Hitech Inquiry Cell of the police started investigations after getting a complaint from the Kerala girl's father who said the matter had caused distress and pain to his daughter.
According to police sources, an unidentified internet user had uploaded the photograph of the 21-year-old girl as the rape victim on the social networking site and lakhs of people liked and shared the photo thinking that it was the picture of the Delhi rape victim.
The girl, whose photograph was uploaded on the site, has the same name which a section of media had given to the Delhi rape victim.
Police suspect that the internet user, yet to be tracked down, might have accidentally come across the complainant girl's profile, copied the image and uploaded it.
However, they are also not dismissing the possibility that the action was undertaken in an attempt to defame her by creating confusion.
Sources in the cyber cell said a case has been registered under Section 66 of the IT Act for spreading defaming messages.
The authorities of the social networking site have been approached to get the details of the account holder who posted the image, they said.