The move comes after a Public Interest Litigation by Shree Rajput Karni Sena.
The protesters, who also took out a motorcycle rally and gathered at outlets in Vjay Nagar and Tukoganj, threatened to ransack them.
The minister, a tribal leader, claimed his statement had been misconstrued and he did not mean to offend anyone.
Shree Rashtriya Rajput Karni Sena on Friday staged a protest and set ablaze the minister's effigy near his official residence here.
Metropolitan Magistrate Rajat Goyal directed the police to answer whether any complaint has been made against the duo by complainant Faizal Ahmed Khan and sought to know what action has been taken.
The makers of Kangana Ranaut-starrer "Manikarnika", on Tuesday said the movie neither distorts historical facts nor does it portray anything objectionable.
The Shree Rajput Karni Sena has been protesting the Deepika Padukone starrer since its inception, claiming the film distorts history.
Shri Rajput Karni Sena on Friday announced it has decided to take back its protest against the release of Sanjay Leela Bhansali's "Padmaavat", stating the movie glorifies the valour of the Rajputs.
The Congress Party today convincingly wrested Mandalgarh Assembly seat and achieved a huge victory in Ajmer and Alwar Lok Sabha seats in the Rajasthan by-polls.
Shri Rajput Karni Sena on Tuesday again claimed that historical facts had been tampered with in the movie.
According to police officers, screening of "Padmaavat" has started in Cinepolis and Mona cinema hall in Patna.
'The nation has gone mad,' said a furious Asha Parekh, the veteran actress who saw 'Padmaavat' a few days back at a special screening organised by the director Sanjay Leela Bhansali.
Padmaavat shows that there was no substance to any of the grievances they have aired over the better part of half a year.
The outfit's leader was detained yesterday for questioning and placed under arrest this morning on charges of breaching peace in the city.
Poonawala, in his plea, has accused four state governments of inefficient management of public order in the cities where the belligerent Karni Sena is carrying out disruptive activities.