"We have detained Sanjeev Jha, as he attempted to break the public peace," a senior police official told IANS.
According to police, the Aam Aadmi Party (AAP) legislator had not taken prior permission to sit on hunger strike outside the Civil Lines house of Mr Mishra.
The police detained Mr Jha after he refused to back off from his decision to sit on protest.
Mr Jha, a legislator from Burari, had on Friday announced he would sit on indefinite hunger strike against Mr Mishra for his "defamatory allegations" against AAP convenor and Delhi Chief Minister Arvind Kejriwal.
Mr Mishra has been on hunger strike since Wednesday at his official residence, demanding that Arvind Kejriwal reveal the source of funding of the foreign trips of five AAP leaders - Sanjay Singh, Ashish Khetan, Satyendar Jain, Raghav Chadhha and Durgesh Pathak - in the last two years.
Mr Mishra was removed as a Delhi minister a week ago in a sudden move and later suspended from the AAP.