A Reuters witness saw at least three drones heading in the direction of the embassy. The C-RAM air defence system shot down two of them while a third struck inside the embassy compound, from which fire and smoke could be seen rising, the witness said.
An explosion was heard in the Iraqi capital, another Reuters witness said.
U.S. embassy mobile phones were switched off when Reuters called seeking comment.
Iranian backed militias have been attacking U.S. interests in Iraq in retaliation for the war which began on February 28.
On Monday, Iran-aligned group Kataib Hezbollah announced the death of its senior commander and spokesperson, and Popular Mobilization Forces said air strikes killed at least eight of its fighters in the Iraqi town of al-Qaim near Syria.
Iraqi security forces have been deployed across parts of the capital and closed Baghdad's fortified Green Zone, which houses government buildings and diplomatic missions including the U.S. embassy.
(Reporting by Maher Nazeh and Ahmed Rasheed; Editing by Tom Hogue and Christopher Cushing)

A general view of the United States Embassy compound after a reported missile strike, in Baghdad, Iraq, 14 March 2026, amid military escalations involving the US, Israel, and Iran that began on 28 February. The US mission did not immediately comment on the incident. EPA/CEERWAN AZIZ