Five soldiers were also wounded in the shootout in North Kashmir's Bandipora district as a joint army and police team mounted a search following a tip-off that up to three gunmen were in the area, a defence spokesman said.
"During the searches, militants hiding in a house opened fire, triggering off an encounter," Lieutenant Colonel Rajesh Kalia told Reuters.
He said there were no arrests, while the remaining gunmen were unaccounted for.
India is trying to contain a low-level insurgency in its northernmost region that dates back more than a quarter century. Protests flared last year after security forces killed a popular underground separatist leader called Burhan Wani.
India accuses Pakistan of smuggling in men, equipment and counterfeit cash to back separatist fighters - a charge Islamabad denies.
Four militants and two Indian soldiers were among seven killed in a gun battle in South Kashmir on Sunday.
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