The terrorists struck at the police picket in Tujjar Sharief area of Sopore in Baramulla by opening fire, a police officer said.
The police post was also guarding the shrine of Sultan-ul Arifin Makhdoom, the officer said.
One policeman, Constable Fayaz Ahmad, was injured in the attack. He was shifted to a hospital in Sopore town where he succumbed to injuries, the officer said.
A civilian, identified as Abdul Rahim Lone, was also killed in the attack.
The militants snatched the INSAS rifle of the injured cop before fleeing from the scene.
Additional forces have been rushed to the spot.