The soldiers were killed late on Monday when they were fired at by militants hiding in the forests of southern Doda district in Jammu division, the Indian military said on X.
Government forces had been conducting a search based on intelligence input when the shooting occurred.
No insurgent group immediately claimed responsibility for the attack.
The attack was the latest in a flurry of violence in the region.
Last week, five soldiers were killed in the nearby Kathua district when suspected rebels ambushed an army vehicle.
In June, nine people were killed when suspected militants fired at a bus carrying Hindu pilgrims.
Rebel groups have been fighting since 1989 for Indian-controlled Kashmir's independence or merger with neighbouring Pakistan.
Most Muslim Kashmiris support the rebel goal of uniting the territory, either under Pakistani rule or as an independent country.
New Delhi insists the Kashmir militancy is Pakistan-sponsored terrorism.
Pakistan denies the charge, and most Kashmiris consider it a legitimate freedom struggle.
Tens of thousands of civilians, rebels and government forces have been killed in the conflict.
Nuclear-armed rivals India and Pakistan each administer part of Kashmir, but both claim the territory in its entirety.
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