Congress politician Mukarram Khan was arrested on Tuesday, days after police in the Hyderabad region of India's Karnataka state registered complaints against him.
Police said he would be soon produced before the local court.
In a video which went viral, Khan can be heard saying: "We are born and brought up here. We will live and end our lives here in India. Those who oppose the wearing of the hijab will be cut into pieces. One day, all of us will die but don't hurt our [religion]. All religions are equal. No religion should suffer injustice. You can wear anything. Who is stopping you?... but we will not tolerate this."
The southern Indian state of Karnataka has seen an increase in protests since a group of Muslim girls were prevented from entering their classroom in the state's Udupi District in January while wearing the hijab.
In February, protests broke out across the state after more Muslim schoolgirls started wearing the hijab and were consequently forbidden to enter their classrooms. Other educational institutions in the state also banned the hijab on campus.
The issue has been brought up in Karnataka's High Court, which has yet to make any ruling on the subject after a few hearings.
Meanwhile, many Indian politicians have attracted widespread attention by joining the fray. In February, BJP parliamentarian Pragya Singh Thakur warned Muslim women not to wear the hijab in public, saying "it wouldn't be tolerated".
Former Jammu and Kashmir state chief Omar Abdullah recently alleged that hatred for Muslims has been "normalised" in the country, which "no longer celebrates its diversity".
On 13 February, Congress lawmaker BZ Zameer Ahmed Khan, made the bizarre claim that women get raped in the country for not covering their face or wearing the hijab.