Three terrorists were also been killed in the ensuing security operation and the attack that has been claimed by the Jaish-e-Mohammad (JeM) terror outfit.
For decades rebel groups have fought roughly 500,000 Indian soldiers deployed in the territory, demanding independence or a merger of the former Himalayan kingdom with Pakistan.
Police say that a body, suspected to be that of one of the attackers, has been found so far, the Press Trust of India reported.
Some security personnel were also injured. However, flights resumed operating in the afternoon after the security clearance from the police.
More than 70,000 people have reportedly been killed in the conflict since 1989.
The attackers are still on the camp's premises, holed up in a building, BSF officials said.
Officials said the airport, which is on a plateau and encircled by military and paramilitary camps, was safe.More news: Texas Tech hangs tough, falls short to No. 15 Oklahoma State
Authorities have sealed the routes leading to Srinagar airport and operations at the airport have been suspended.
An unspecified number of militants attacked the heavily guarded camp outside the airport in the region's main city of Srinagar, hurling grenades and spraying automatic gunfire, said top officer S.P. Vaid.
On 26th of August, fidayeen militants stormed the District Police Lines in south Kashmir's Pulwama district. The camp was located near Srinagar International Airport.
In the initial reports it is not revealed if the militants managed to enter the camp or they started firing from the outside.
Last week, Pakistan said three civilians were killed on their side of the de facto border in Kashmir after Indian soldiers opened fire.
Khan, who heads the police force in the Kashmir Valley, denied that there had been a security breach that led to the attack.
"I have spoken to the DG, CRPF, and DG, BSF".