The U.S. Joint Operations Command said in a statement that a total of five rockets crashed near the embassy without causing any injuries, but according to a security source cited by the AFP, three of the rockets "directly hit" the building with one striking a cafeteria at dinner time.
It was not immediately clear who carried out the attack.
"We call on the government of Iraq to fulfill its obligations to protect our diplomatic facilities," a State Department spokesperson said in a statement, urging Iraq to protect the embassy.
The attack was the third in a series of such strikes on the U.S. embassy so far this month. However, it was the first time the building was directly hit.
Iraqi Prime Minister Adel Abdul Mahdi immediately condemned the incident in a statement, and called it an "aggression" that could "drag Iraq into becoming a war zone."
In the meantime, one protester was killed in the capital and more than 100 demonstrators were wounded in clashed with the security forces in several cities including the capital, according to Reuters.
Iraq’s anti-government demonstrations started in October and were re-ignited a week ago after weakening since the beginning of the month amid the geopolitical crisis that followed the assassination on Jan. 3 of top Iranian Major, General Qassem Soleimani in a U.S. strike in Baghdad.
The people protesting in Iraq have been calling for an overhaul of a system they deem deeply corrupt and the removal of a ruling elite that has been controlling the country since the U.S. invaded the country in 2003.
They are demanding early elections based on reformed voting law, a new prime minister to replace current caretaker Abdel Mahdi and alleged corrupt officials to be judged.
At least 12 demonstrators have been killed since last Saturday, the Iraqi High Commission for Human Rights said. In total, at least 500 protesters have been killed since October.