Superintendent of Police, Sopore, Imtiyaz Hussain told PTI that "Militants opened fire on a police party while they were clearing the traffic jam in Iqbal market area in Sopore."
He said constable Kishor Kumar was hit by a bullet in the neck while an elderly civilian was also injured in the attack.
The civilian later succumbed to injuries.
The militants snatched the service rifle of the injured cop before fleeing from the scene, he said.
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Efforts are to track down the assailants.
The attack comes three days after militants attacked a BSF convoy in the outskirts of Srinagar city, leaving a jawan dead and two others injured.
On March 13, Lashkar-e-Toiba militants, disguised as cricketers, had attacked a CRPF camp in Srinagar city, killing five of its personnel.
Two militants were killed in retaliatory action, while police arrested four persons including a Pakistani national in the course of investigations into the attack.
On March 2, two policemen were shot dead by militants in Kupwara district of north Kashmir.