The gunfight erupted at Beighpora in Awantipora, some 32-km from here, after militants fired at an army patrol at around 7.00 pm, they said.
An AK 47 rifle and some ammunition were recovered from the scene.
Police said the identity and group affiliation of the militant was being ascertained but according to intelligence sources, the dead was Irshad Ahmad, a top LeT militant.
He was believed to be involved in the attack on an army convoy at Hyderpora in June last year in which eight soldiers were killed and others 16 injured.