Six policemen were also wounded in the attack on the camp in Sopore town on Saturday, 30 miles north of Kashmir’s summer capital Srinagar.
A group known as Al-Mansurian said it carried out the attack, which began on Friday and lasted for 24 hours.
Indian security agencies say Al-Mansurian is the new name of Lashkar-e-Taiba, an outlawed Pakistan-based group.
The separatists are fighting Indian rule in Kashmir.
“The fierce firefight ended today (Saturday) at 5:30am and the search operation of the camp building is continuing,” Faruq Ahmad, a police officer in Sopore, said.
Ahmad said the body of one of the separatists had been recovered from the building, which was damaged in the encounter.
“It is still not clear how many militants were involved in the attack,” Ahmad added.
Islamabad denies India‘s allegations that it is supporting the 15-year-old revolt in Kashmir but says it provides moral and diplomatic support to Kashmiri “freedom fighters”.
Pakistan says it gives only moral
The countries, which both claim the Himalayan region, have fought two wars over the disputed territory.
Last month, New Delhi began to withdraw a small number of its more than 400,000 troops in Kashmir, citing a drop in separatist attacks and a decline in incursions from Pakistan.
Pakistan denies giving material support to the separatists.
At least 45,000 people have been killed since an armed insurgency broke out in the region in 1989, according to Delhi. Separatists put the figure at twice that.