Other 17 soldiers were injured, an army spokesman said, adding that no one is missing and rescue teams have returned to their bases.
Dozens of troops were rescued after the avalanche struck near Gulmarg, the region's main ski resort, about 50km (30 miles) west of Srinagar.
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.
This is one of the deadliest avalanches to occur in the region in recent years.
Last June seven Indian soldiers were killed in an avalanche in Kupwara district. Another 12 people were killed a month earlier on the Pakistani side of the heavily-militarised dividing line.
In 2005, an avalanche near villages in the Neelum valley on the Pakistani side killed more than 40 people.