The shootout began when soldiers cordoned off a neighbourhood in the northern area of Hajin after a tip-off that armed militants were hiding there, said army spokesman Colonel Rajesh Kalia.
"Six terrorists have been killed in the encounter," Kalia told AFP.
"One IAF (India Air Force) soldier was martyred and another army soldier was injured."
On Friday a militant and a police officer were killed in the outskirts of the main city of Srinagar during a brief shootout.
Kashmir has been divided between India and Pakistan since the end of British colonial rule in 1947. Both claim the former Himalayan kingdom in full.
Rebel groups have for decades fought Indian soldiers and paramilitaries deployed in the disputed region, demanding independence or a merger of the territory with Pakistan.
The fighting has left tens of thousands, mostly civilians, dead.
India accuses Pakistan of sending fighters across their de facto border in Kashmir to launch attacks on its forces.
Islamabad denies the allegation, saying it only provides moral and diplomatic support for the Kashmiri struggle for the right to self-determination.
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