"We will never tolerate any attack on the Pakistan army," he said in televised remarks.
Police official Zubair Ahmed said the attacker detonated his explosives after guards stopped him at the barracks gate. He said the dead and wounded had been transported to a military hospital.
More than 600 people have been killed in Pakistan in attacks by militants, many of them targeting the government, since mid-October, when the army launched a major offensive against the Pakistani Taliban's stronghold of South Waziristan in the northwest.
But attacks are rare in Kashmir, which is divided between Pakistan and India and claimed by both in its entirety. Most of the militants operating in the Himalayan region attack Indian targets because they seek to end New Delhi's rule. They use the Pakistani side to plot attacks, but rarely strike there.
However, on Dec. 28, a suicide bomber attacked a Shiite procession in Muzaffarabad, the capital of Pakistan-administered Kashmir, killing eight people and wounding another 80.
There was no immediate claim of responsibility for Wednesday's attack in Kashmir.