The shootout took place near the de facto border with Pakistan, although it was not immediately clear whether the dead fighter had crossed into India from there.
India regularly accuses Pakistan of arming and sending rebels across the border known as the Line of Control to launch attacks on its forces -- allegations which Islamabad denies.
"Two BSF (Border Security Force) soldiers were martyred and a terrorist was killed in the gun battle," army spokesman N.N. Joshi told AFP.
Kashmir has been divided between India and Pakistan since the two won independence from British rule in 1947.
Several rebel groups have for decades been fighting an estimated 500,000 Indian soldiers deployed in the restive territory, demanding either independence for the region or its merger with Pakistan.
Tens of thousands have died in the fighting since 1989 when the armed rebellion against Indian rule over the Himalayan territory began.
Large parts of the restive territory including Srinagar have been under a strict curfew for the past month following widespread anti-India protests, sparked by the killing of a popular young rebel leader in a gunfight with government forces.
At least 55 civilians and two police have been killed in the latest unrest, the worst since 2010, and nearly 5,000 protesters and bystanders have been injured.