In the retaliatory fire from the Army, Two terrorists were also killed in the attack.
"Army jawans who were injured in the attack have been shifted to Srinagar for treatment".
A group of militants stormed a military camp close to the heavily militarized Line of Control dividing the Himalayan region of Kashmir between India and Pakistan, army spokesman Col. Rajesh Kalia said.
"My heartfelt condolences to the families of our three fearless soldiers martyred in the Kupwara attack", he added. "Two attackers were also killed in the gunfight", the official said.
The operation to hunt down other terrorists is still on, PTI said.
Clashes between rebels and government forces have become more frequent since the killing of a popular rebel leader, Burhan Wani, by Indian security forces last July which sparked widespread unrest.
Reports said the army is busy in combing operations right now. No militant outfit claimed responsibility for the attack.
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A year ago in September, terrorists, believed to belong from Pakistan, had attacked an army camp in Uri leaving 19 soldiers dead.
Seven other soldiers were also wounded in the strike.
Around 4.40 in the morning, the terrorists entered the Kupwara Army camp from the rear side of the firing range.
"3 soldiers martyred, dreams of 3 families shattered, as we were sleeping".
He said since three AK-47 rifles have been recovered, army is probing whether three militants were involved in the attack and one of them managed to escape.
Three Indian soldiers killed in Pakistan BAT attack in Machhal sector of Kupwara district along the LoC, with body of one decapitated.