The case was registered by a person named Navneet Chahal, a resident of Lakhori Jalalpur village, the police said.
"In his complaint, Chahal alleged that on his Facebook wall, one Sahil had posted an objectionable photo of Chief Minister Yogi Adityanath," said Devendra Sharma, in-charge of Nakhasa police station in Uttar Pradesh's Sambhal district.
The officer added that Chahal claimed the post had provocative comments that hurt his sentiments.
In March, the Bengaluru police had lodged a criminal case against a woman for making "objectionable posts" on her Facebook page, which depicted Yogi Adityanath in "poor light".
The complaint was filed by the BJP's youth wing - BJP Yuva Morcha - which claimed that the woman, identified as Prabha N Belavangala, is a "habitual mischief and rumour mongrer" who has tried to create societal disharmony by publishing inflammatory content on Facebook.
A similar complaint was also registered against a man in Noida, identified as Rahat Khan, for posting objectionable images and comments about Chief Minister Yogi Adityanath. The complaint was filed by the Hindu Yuva Vahini, an outfit founded by the Chief Minister.
Yogi Adityanath is the mahant or head priest of the Gorakhnath Math, a temple in Gorakhpur. He is a five-time Lok Sabha member from Uttar Pradesh's Gorakhpur constituency and he took oath as Chief Minister following the BJP's thumping victory in the state.
(with inputs from PTI)