The militants targeted the police officer guarding the shrine of Tujjar Sharif, 55 kilometres (35 miles) northwest of the main city of Srinagar.
"The policeman unfortunately lost his life, and a civilian who was shot during the attack succumbed to his injuries later," deputy inspector general of police for the area, Gharib Das, told AFP.
"It appeared that the policeman on guard was the target, not the shrine."
Read: Woman killed by Indian shelling in Kashmir
It was not clear if the 70-year-old disabled civilian was shot by the militants or he was hit by a bullet when police returned fire.
The militants fled the area after the attack and the dead police officer's automatic rifle was missing, Das said, adding security forces had launched a hunt for the attackers.
Rebels in recent years have often attacked lone police officers on duty and snatched their service weapons.
Last week a bomb hidden in a steel pot exploded inside the compound of a mosque in the southern Kashmir valley, injuring ten people. No rebel group claimed responsibility for the rare explosion.
Read: Kashmiris mark India’s independence as black day
Pakistan and India have exchanged heavy mortar fire across their disputed border in Kashmir almost daily since last week. A total of eight civilians on both sides have been killed and many injured.
The cross-border exchange of fire continued Tuesday in the southern Poonch sector of the region, said India's defence ministry spokesperson Manish Mehta.
COMMENTS (1)
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ