Security forces managed to repulse the attack on the complex, which serves as a training academy for airport security forces.
The Pakistani military said troops were sent to help the security forces after the shooting by two men on a motorbike who fled.
A senior official with the Airport Security Force, Colonel Tahir Ali, said: "We cannot take any risks and allow terrorists to get into our facility. Whenever there is such an incident, we will react forcefully."
A spokesman for the Pakistani Taliban claimed responsibility.
The attack came after a siege on Sunday night by Taliban militants who stormed a VIP and cargo terminal at the airport in an attack that killed 36 people, including the 10 gunmen and at least 11 members of the Airport Security Force.
Pakistani authorities were still discovering bodies from that siege yesterday. Airport authorities found seven bodies in a burned building. The discovery inside a cold storage unit, a day after Pakistani officials said the airport had been secured, is sure to raise more questions about security at the country's busiest airport.