Dozens of troops were rescued after the avalanche struck near Gulmarg, the region's main ski resort, about 50km (30 miles) west of Srinagar.
The army said 17 soldiers were injured. Rescue teams have returned to base.
Avalanches are common in Kashmir, but this is one of the deadliest to occur in the region in recent years.
About 400 troops were stationed at the high-altitude camp, part of which is said to have been engulfed in snow.
Tourists were unaffected by the avalanche because it happened at a higher altitude than the nearby ski resort, officials said.
The soldiers were on a training exercise at the Indian army's high altitude warfare school, nearly 3,000m (more than 9,000ft) above sea level in the Khelenmarg mountains.
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