Alliance spokesman Colonel Wayne Marotto said on Twitter that the "Ain Al-Asad Air Base (AAAB) was attacked by an unmanned aerial surveillance system" at around 11.30 p.m. on Friday, dpa news agency reported.
"No injuries reported. A hangar was damaged. The attack is under investigation," he added.
So far, there has been no claim of responsibility for the attack.
It was the latest in a series of attacks targeting bases housing US forces in Iraq.
In recent months, the heavily-fortified Green Zone in the capital Baghdad, home to the US embassy, and facilities hosting American troops in Iraq have been the target of repeated attacks blamed on pro-Iranian groups.