Srijato Bandopadhyay posted his 12-line poem "Abhishap" or Curse on Sunday, the day Yogi Adityanath was sworn in as Chief Minister. The poem uses the term 'yogi' and words rhyming with it.
The poem has had over 7,500 likes, 3,000 plus comments and nearly 2000 shares on Facebook. It has also drawn a flood of angry and disturbing comments that Mr Bandopadhyay says are very "dangerous and threatening".
The Kolkata-based poet has written lyrics for many popular Bengali films and also won the prestigious Ananda award in 2004.
"It is really sad that in a country like India, which is known for its democratic values, the right to freedom of speech and expression is shrinking fast. The majority of people in this country believe in freedom of speech," Mr Bandopadhyay said on Tuesday.
Complainant Arnab Sarkar, a resident of Siliguri, said, "As a Hindu, my sentiments were hurt by the poem. The police took my complaint very reluctantly. They said nothing would come of it. Let's see. If a person from another religion had wanted to file this complaint, I think there would be no problem."
Mr Sarkar said he is a member of Hindu Samhati, a non-political organization which is active in many parts of Bengal. He filed the complaint with the cyber cell of the Siliguri Police last night.