The overnight killings took place during a search operation following a tip in Ganie-Hamam area, an official statement said on Wednesday.
The security forces were fired at by hiding terrorists, triggering the gun battle in which SPO Bilal Ahmad and Sub-Inspector Amardeep Parihar were injured, it said.
Ahmad succumbed to his injuries while Parihar was warded at the Army hospital. "We pay our rich tributes to Martyr Bilal who made the supreme sacrifice in the line of duty."
The terrorist was identified as Momin Gojri, a resident of Baramulla.
"The killed terrorist was affiliated with proscribed terror outfit LeT and was wanted for his complicity in a series of terror crimes. As per police records, he was involved in planning and executing several terror attacks in the area and many other civilian atrocities. Several terror cases were registered against him," the statement added.
It said arms and ammunition were recovered from the site.
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," the statement said.
"People are requested to cooperate with police till the area is completely sanitized and cleared of all the explosive materials if any," it said.
The CRPF, Army and the Special Operation Group of the Jammu and Kashmir Police were involved in the operation.
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 Jammu and Kashmir and Ladakh.
( With inputs from IANS )