The case was filed by a lawyer in the court of the chief judicial magistrate (CJM) and alleges the "Har har Modi, ghar ghar Modi" slogan, which likens Modi to Lord Shiva, hurt his religious sentiments.
Petitioner Manoj Dubey said this slogan was coined to garner electoral gains during the Lok Sabha election in which the Gujarat chief minister is a contestant from Varanasi.
"I had petitioned the Election Commission also on the matter but no action was taken. I have now decided to take the matter to the court," Dubey told IANS Tuesday.
The court has sought a detailed report from the police over the issue.
The Bharatiya Janta Party had come under fire for using the slogan.
The party later distanced itself from the controversial slogan.
The party has now coined a new slogan -- "Dil dil Modi, ghar ghar Modi, kan kan Modi" (every heart, house and particle has Modi) for the local campaign of the party in Varanasi.
The next hearing of the case has been fixed for April 3.