Two Iraqi security officials said at least four rockets were launched on Thursday against the US Embassy in Baghdad's strongly protected Green Zone.
The region is home to diplomatic missions and the Iraqi government's headquarters. According to officials, three of the missiles struck within the perimeter of the American Embassy, and another struck a nearby residential complex's school.
The officials spoke on the condition of anonymity due to their lack of authority to talk with the media.
According to an Iraqi military statement, the attack injured a girl and a mother but provided no additional details. According to the report, the rockets were launched from Baghdad's Dora neighborhood.
During the attack, witnesses reported hearing the embassy's C-RAM defensive system designed to detect and destroy incoming rockets, artillery, and mortar rounds.
The attack is the latest in a series of rocket and drone strikes on the American presence in Iraq since the beginning of the year, marking the second anniversary of the US strike that killed Iranian General Qassim Soleimani and Iraqi militia commander Abu Mahdi al-Muhandis.
A spate of assaults last Thursday targeted American forces in Iraq and Syria. Rockets attacked an Iraqi military base housing US forces in western Anbar province and the city.
Pro-Iran Shiite factions in Iraq have sworn vengeance for Soleimani's assassination and have tied the termination of the attacks to the complete withdrawal of American soldiers.
Last month, the US-led coalition announced the formal end of its combat mission, assisting Iraqi forces in their ongoing struggle against the Islamic State organization.
Around 2,500 troops will remain as the coalition transitions to an advising role to assist Iraqi security forces.
Marine Gen. Frank McKenzie, the top US commander in the Middle East, warned last month in an interview with The Associated Press that he anticipates increased attacks on US and Iraqi personnel by Iranian-backed militias trying to drive American forces out.