The convoy was attacked in Machedi area of Kathua district, about 300 km south of Srinagar, the summer capital of Indian-controlled Kashmir.
Militants reportedly first lobbed a grenade and then resorted to heavy firing, which was retaliated by the troopers.
"A total of 10 troopers were wounded and four of them later succumbed to their injuries," a local newspaper quoted an official as having said.
The remaining six are said to be undergoing treatment at a hospital.
Reports said following the attack, the militants managed to escape into the nearby forest.
Authorities have rushed reinforcements to the area to trace the militants.
MNA/PR