Two army vehicles were conducting an operation in Rajouri district south of Srinagar, the region's biggest city, when they were fired upon by rebel forces, a defence spokesperson told AFP.
"Troops sustained 3 fatal and 3 non-fatal casualties," the spokesperson added.
Army operations were continuing in the area and further details of the incident were "being ascertained", they said.
Kashmir has been divided between India and Pakistan since both countries gained independence in 1947, with each claiming the high-altitude territory in full.
The fighting comes just days after India's top court upheld a 2019 decision by Prime Minister Narendra Modi's government to revoke the limited autonomy of the Muslim-majority territory.
Rebel groups have waged an insurgency in the Indian-controlled portion of Kashmir since 1989, demanding independence or a merger with Pakistan.
The conflict has left tens of thousands of civilians, soldiers and militants dead.
Last month, five Indian soldiers and two suspected rebels were killed in the region.
India blames Pakistan for backing the militants, a charge Islamabad denies, saying it only supports a Kashmiri struggle for the right to self-determination.
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