Many rockets landed at the Ain Assad military airbase that houses Iraqi and US-led coalition forces in Iraq’s western Anbar province, with no casualties reported initially.
US and Iraqi forces are housed at the base in the western Anbar province, as well as troops from other members of the Operation Inherent Resolve coalition against the "Islamic State" (IS) group.
The US last week launched an airstrike in eastern Syria on facilities used by Iran-backed militia.
About 13 rockets were launched from a location some 8 kilometers (5 miles) from the base, a Baghdad Operations Command official told the Reuters news agency.
The rocket attack was the second in Iraq this month, coming two days before Pope Francis is due to visit the country.
A rocket attack on US-led forces in northern Iraq last month killed a civilian contractor and injured a US service member.
Militants apparently backed by Iran fired numerous missiles at two bases that were hosting US forces, including Ain al-Asad, last January.
Tehran said the attacks, which caused injuries among US personnel, were in revenge for the assassination of General Qassem Soleimani, leader of the Islamic Republic's elite Quds force.
Rocket attacks were also carried out on other American targets in Iraq since then, including the US Embassy in Baghdad.
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