The Al Asad airbase, which hosts American troops, was hit on Saturday night - with an unspecified number "undergoing evaluation for traumatic brain injuries".
At least one Iraqi service member, who was stationed at the base, was also wounded in the attack, the US Central Command has said.
The statement added: “Iranian-backed militants fired several shells and ballistic missiles" at the base, saying defence systems "intercepted most of the missiles, while others fell on the base".
An Iraqi military official said 12 missiles were fired at the base, of which four were shot down and eight fell within the base.
A coalition of rebel groups calling itself the Islamic Resistance said it had launched a missile salvo at the base.
The group reportedly emerged in late 2023 and is one of several Iran-tied groups that is operating in Iraq.
The US on Saturday also carried out fresh air strikes against a Houthi anti-ship missile which it said was a threat to ships in the area.
In a statement on Saturday, US Central Command said the missile "was aimed into the Gulf of Aden and was prepared to launch".
"US forces determined the missile presented a threat to merchant vessels and US Navy ships in the region, and subsequently struck and destroyed the missile in self-defence," the statement said.
"This action will make international waters safer and more secure for US Navy and merchant vessels."
The Iranian-backed Houthis did not immediately acknowledge the seventh round of strikes.
The rebels have been targeting shipping since November in what they describe as an effort to stop the Israel-Hamas war.
Meanwhile, the British government has said Royal Navy missiles that have been used to shoot down Houthi drones in the Red Sea will be upgraded. Pakistan has this week also launched strikes on Iran-based insurgents.