Singh is the leader of the BJP in Uttar Pradesh assembly, while Som is the MLA from Sardana. Rakesh Tikait and Naresh Tikait are top Bharatiya Kisan Union leaders.
It was not immediately clear what charges these leaders would be booked under, but a police official who did not want to be named said there was a clear case of violation of the administration's prohibitory orders clamped under section 144 CrPC.
Locals fear the FIRs against the leaders could stoke fresh unrest.
Violence erupted after people returning from the meeting held at Nagla Mandor village under Sikhara police station were attacked.
The meeting had been convened over the murder of two people of a community. The two murders followed the killing of a man from another community on August 27 over alleged vulgar remarks passed at a girl.
Meanwhile, Shamli adjoining Muzaffarnagar witnessed a flag march by the army on Sunday evening. Several villages in Muzzafarnagar and Shamli districts saw violence and arson.