The FIR, accusing Facebook users of uploading and circulating the morphed photo, was registered on Pradeep Bakhale's complaint.
Dhavalikar had attracted controversy when he recently said: "Young girls wearing short skirts in nightclubs are a threat to the Goan culture. This habit of young girls wearing short dresses everywhere does not fit the Goan culture. We should not allow this. It should be stopped."
He also advised that women should stop drinking too "because it is not good for their health".
The comments had attracted criticism with the Congress symbolically gifting Dhavalikar a short pink skirt in response.
A couple of months back, an FIR against shipbuilding professional Devu Chodankar for accusing then BJP's prime ministerial candidate Narendra Modi of planning a holocaust on Facebook had led to prompt police action.
The police action also earned criticism from civil society as well as the opposition which accused the police and state administration of muffling the internet.