Police said the troops fired Tuesday after villagers pelted them with stones in the southern Shopian area.
Clashes were also reported in at least two places in the northern Bandipore area, AP reported.
The killing of a popular rebel commander on July 8 has sparked some of Kashmir's largest protests against Indian rule in recent years.
A strict curfew, a series of communication blackouts and an intensified crackdown have failed to stop more than six weeks of deadly protests. Residents have struggled to cope with shortages of food, medicine and other necessities.