There have been no civilian casualties or collateral damage, the Army said.
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.
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.
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.
Modi is scheduled to visit Palli village of Samba on National Panchayati Raj Day on April 24.
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.