The incident took place on Wednesday night at a military camp about 20km (12 miles) north of the city of Srinagar.
An investigation was underway to determine the cause of the incident, officials said.
Kashmir is divided into Indian and Pakistan-administered sides, but both sides claim the region in full.
Both station troops there and there are periodic incidents, although a ceasefire along the line of control, which divides the region, was agreed in November 2003.
Thousands of people have been killed in Indian-administered Kashmir since an armed revolt against Indian rule erupted in 1989.
Indian media said soldiers stationed in the region often complained of long working hours, in poor conditions and with inadequate leave.