The overnight killings took place during a search operation in Ganie-Hamam area, an official statement said on Wednesday.
The statement said that security forces were fired at by hiding terrorists, triggering the gun battle in which SPO Bilal Ahmad and Sub-Inspector Amardeep Parihar were injured.
Ahmad succumbed to his injuries while Parihar is warded at the Army hospital. "We pay our rich tributes to Martyr Bilal who made the supreme sacrifice in the line of duty."
The body of a terrorist was retrieved from the site but his identity is not known yet. Security agencies recovered arms and ammunition there.
The security forces urged civil not to step into the battle zone.
"Citizens are requested not to venture inside the encounter zone since such an area can prove dangerous due to stray explosive materials. People are requested to cooperate with police till the area is completely sanitized and cleared of all the explosive materials if any," the statement said.
The search operation followed a tip off. Involved in the operation were the CRPF, Army and the Special Operation Group of the Jammu and Kashmir Police.
This is the first gun battle between security forces and militants since Article 370 was axed and Jammu and Kashmir was split early this month into two Union Territories.
( With inputs from IANS )