Two other Indian soldiers were wounded in the clash that took place in the Tral area.
"Our forces launched a search operation based on a tip-off in Hadoora village on Tuesday afternoon," a senior police official told The Anadolu Agency. "Fighters in the village fired on the joint search team, starting an intense gun fight."
According to the Indian army, one of the slain was a colonel who received a bravery award a day earlier on the country's Republic Day.
Kashmir, a Muslim-majority Himalayan region, is held by India and Pakistan in parts and claimed by both in full.
The two countries have fought three wars -- in 1948, 1965 and 1971 -- since they were partitioned in 1947, two of which were over Kashmir.
Since 1989, Kashmiri resistance groups have been fighting against Indian rule for independence or for unification with neighboring Pakistan.
More than 70,000 people have been killed in the conflict so far.