The complaint was filed after the woman said her portrait was taken without consent and later overlaid with Modi's visage for banners that fluttered over Jantar Mantar.
The protest, which kicked off on June 20, saw the CJP march toward Parliament before clashing with security forces; tear gas and batons were deployed as the demonstrators pressed forward.
While the FIR names "unknown persons" as accused, the complaint also names CJP founders Abhijeet Dipke, Saurav Das and Ashutosh Ranka, none of whom appear on the police file.
Police say the matter is being investigated from all angles, noting that the altered image was also circulated on Instagram and other social media.
The woman says the misuse of her likeness has damaged her dignity, and she alleges she was threatened by protestors.
With the protest ending on July 25 after former Education Minister Dharmendra Pradhan resigned, the investigation is now the sole avenue for any legal action.
Police are expected to file formal charges once the forensic analysis of the image is complete, but no arrests have been announced.