One militant was killed in the exchange of firing, Director General of Police SP Vaid said.
The attack took place at 4.00 am and exchange of firing is still on between the militants and security forces, they said.
The terrorists are holed up inside the building campus of the 182nd Battalion camp, BSF officials said.
Airport operations have been suspended as the security forces were fighting militants who had breached into the 182 battalion headquarters of BSF located in Gogoland, police said.
This battalion is entrusted with security of runway of the Srinagar airport.
The area also houses training centres of the BSF and CRPF.
Schools in the vicinity of the airport have been closed.
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