Operation has been launched and further details being ascertained, the spokesman said without giving details about the assailants who fired on the sentry post.
According to officials, Naik Kuldeep Singh of Punjab was on guard duty when he was hit by a bullet in the head at Sunjawan Military Station on the outskirts of Jammu and was evacuated to a hospital where he succumbed to injuries.
There have been no civilian casualties or collateral damage, the Army said.
On Friday, an attempt by the banned terror group Jaish-e-Mohammed to carry out a suicide attack ahead of Prime Minister Narendra Damodardas Modi's visit was foiled after two suspected Pakistani terrorists were killed in Jammu in an encounter in which a Central Industrial Security Force officer also died.
The court agreed to re-constitute a five-judge bench to hear pleas after summer vacation.
An alert has also been sounded along the border and a high degree of vigilance is being maintained at vital installations in Jammu and Kashmir in view of the visit, they said.
Modi is scheduled to visit Palli village of Samba on National Panchayati Raj Day on April 24.
Both the terrorists, equipped with suicide vests and sophisticated weapons, were killed in the encounter on Friday, averting a major suicide attack in the city.
Two terrorists carried out a 'fidayeen' attack on an Army camp in Jammu's Rajouri district in the early hours of Thursday, killing three soldiers.
Here's a recap of moments captured in India in the last week.
Mudasir Ahmed Khan alias 'Mohd Bhai, an electrician with a graduate degree and a resident of Pulwama, arranged the vehicle and explosives used in the terror strike.