The 21-year-old man was killed during clashes in Anantnag district south-east of the main city of Srinagar, in which police said scores were injured.
There have been weeks of deadly unrest in the region.
“Naseer had a zero degree pellet injury near his heart. That means he was shot from very close range,” an unnamed medical superintendent at Seer Hamdan hospital in Anantnag said.
Home Minister Rajnath Singh said on Monday police and troops would use chilli-based shells instead of the ones filled with birdshot to quell the unrest after hundreds of civilians sustained serious eye injuries in the clashes.
The government has been coming under growing pressure over the level of casualties in Kashmir during the protests against Indian rule, which broke out after the death of a popular separatist leader on July 8 in a gunbattle with Indian troops.
More than 90 civilians have been killed and thousands injured in the worst violence to hit the Muslim-majority territory since 2010.
The metal pellets or birdshot fired from the pump-action shotguns rarely result in deaths, but can often blind victims if the fragments hit them in the eye.
Authorities lifted a curfew in most parts of the territory late last month, but schools, shops and many banks remain closed while residents struggle with a communications blackout.
Kashmir has been divided between India and Pakistan since the two gained independence from British rule in 1947. Both claim the territory in full.
Several groups have for decades fought Indian soldiers – currently numbering around 500,000 – deployed in the territory. They demand independence for the region or its merger with Pakistan.
Tens of thousands of people, mostly civilians, have died in the fighting.