Government forces have responded by imposing round-the-clock curfews and using live ammunition and tear gas to disperse the protesters.
The recent unrest in Kashmir, divided between India and Pakistan and claimed by both, is reminiscent of the late 1980s, when protests against New Delhi's rule sparked an armed conflict that has since claimed 68,000 lives.
Soon after Tuesday's shooting, fresh protests erupted in the area with residents chanting slogans "Go India! Go back" and "We want freedom".
Hundreds also defied the curfew in the western Kashmir town of Budgam and held a protest march.
Government forces fired live ammunition and tear gas to disperse the protesters, injuring four people, a police officer said.
He said the army was also patrolling the main highways in the region to stop protesters from blocking them.
Last week, local authorities asked two retired judges to investigate the deaths of protesters, but the move has failed to placate some Kashmiris.
India and Pakistan have fought two wars over control of Kashmir since they gained independence from Britain in 1947.
Kashmiri separatists reject Indian sovereignty over the region and want to carve out a separate homeland or merge with predominantly Muslim Pakistan.