Neemuch-based senior journalist Jinendra Surana wrote on his Facebook wall: "Get raped in Madhya Pradesh to get the Padmavati award. The government's new announcement."
The post got a lot of comments on the social media site.
Khargone Deputy Inspector General AK Pandey told IANS: "Surana's post was obscene and could have instigated others to commit similar crimes. Consequently, taking suo moto cognizance of the incident, we registered an FIR."
He said the probe is on and police is trying to see what action can be taken against those who commented on the post.
Mr Surana has defended his post saying he was being "sarcastic", and said if sarcasm and humour are treated as criminal offences, people will stop speaking their mind.