The evening attack on Al-Balad did not cause any casualties or damage inside the base, the security official said.
According to AFP the other five rockets crashed into a nearby village, the source added, noting that all seven were fired from a separate village in the neighbouring province of Diyala, east of the base.
There was no immediate claim of responsibility.
There have been several such attacks in recent weeks targeting locations where US forces operate.
On March 3, an American sub-contractor was killed in a similar attack against another airbase, Ain Al-Assad, in Iraq's western desert.
That came days after the US bombed a border depot in neighbouring Syria which the Pentagon said was used by Iraqi armed militia that have been tied to the rocket attacks.
Dozens of rocket attacks and roadside bombs targeted Western security, military and diplomatic sites in Iraq in 2020, blamed by Iraqi and Western military sources on hardline factions.
The attacks had come to a near-complete halt in October following a truce with the hardliners, but have since resumed.
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