There are no reports of immediate casualties.
The US has blamed Iran-backed paramilitary groups for a spate of similar attacks in recent months on the Green Zone, but there has never been a claim of responsibility.
Earlier this month, two military bases housing US troops in Iraq came under fire from at least a dozen ballistic missiles, triggering a heightening of tensions between the US and Iran.
Iranian state TV said Tehran had launched "tens" of surface-to-surface missiles at the Al Asad airbase in response to America's killing of Qasem Soleimani, a top Iranian general.
On Monday this week, newly appointed commander of Iran's elite Quds Force, Esmail Qaani, remarked that Iran would "hit its enemy in a manly fashion" in retaliation.
"(The US) hit (Soleimani) in a cowardly way, but with God's grace and through endeavours of freedom-seekers around the world who want vengeance over his blood, we will hit his enemy in a manly fashion," he said yesterday.
Iran's Supreme Leader Ali Hosseini Khamenei has called for the expulsion of all American troops from the Middle East.