Four Katyusha rockets struck a military base next to Baghdad International Airport on Monday wounding “six fighters”, a statement from the military said.
Security forces found launchers with rockets that had not been fired properly, indicating a larger attack was planned, it added.
Security sources told AFP that the wounded in Monday's attack belong to Iraq's Counter-Terrorism Service, an elite unit that was created and trained by US forces.
Two of them are in critical condition, the sources said.
There have been at least nine attacks against US targets in Iraq in the span of six weeks.
There have been no claims of responsibility and no US forces have been wounded.
US defense officials have blamed several of the attacks on Iran-backed factions in Iraq.
On Thursday, two Katyusha rockets landed inside Balad air base, but there were no casualties or damage reported from the attack.
Balad base hosts US forces and contractors and is located about 80 kilometers (50 miles) north of Baghdad.
On Tuesday, five rockets landed on Ain Al-Asad air base, which hosts US forces in Anbar province in western Iraq without causing any casualties.
Tensions between Iran and the US have soared since Washington pulled out of a landmark nuclear agreement with Tehran last year and reimposed crippling sanctions.
US officials say they are considering plans to deploy between 5,000 and 7,000 additional troops to the region to counter Iran.