The attack took place on Sunday evening when unidentified militiamen fired the two rockets, one of which landed on the edge of the airport in the southwest of the capital Baghdad, the media office of the Iraqi Joint Operations Command said in a statement.
The air defence in the area managed to shoot down the other rocket, Xinhua news agency quoted the statement as saying.
An Interior Ministry source told Xinhua that sirens wailed during the attack in a military base housing US forces near the airport, without giving more details.
No group has so far claimed responsibility for the attack.
The Iraqi military bases housing US troops across Iraq, as well as the American Embassy in the Green Zone, have been frequently targeted by mortar and rocket attacks.