The clash broke out when the members carrying the procession, which was on its way to Karbala, took a wrong route other than the specified one, police said.
The members from the other community objected to the procession's course, police said.
Later, the two clashed with each other and indulged in brick-batting and firing under Bithri Mainpur police station area, police added.
Seven people received minor injuries, with senior police officials rushing to the spot and additional forces being deployed to control the situation, police said.