The two staff members, who spoke on condition of anonymity because they were not authorized to brief the media, did not specify the injured person's nationality or the severity of their wounds. They said the rocket slammed into a restaurant inside the embassy compound.
Violent clashes between Iraqi security forces and anti-government protesters also continued to seethe overnight, with one protester shot dead in a violent crackdown in the country's south.
The U.S. Embassy is within the Iraqi capital's Green Zone, and has been a flashpoint amid wider regional tensions between the U.S. and Iran, which have played out inside Iraq in recent weeks. Iraqi supporters of an Iran-backed militia stormed the embassy compound on Dec. 31, smashing the main door and setting fire to the reception area.
At least five katyusha rockets landed inside the Green Zone on Sunday, according to a U.S. military statement. It was the third rocket attack targeting the U.S. Embassy this month, and the perpetrators were not immediately known. Previous attacks caused no injuries.
The U.S. has accused Iran-backed militias of targeting U.S. interests by attacking military bases housing Americans and diplomatic missions.
Iraqi Prime Minister Adel Abdul-Mahdi condemned the attack in a statement, asserting Iraq's commitment to protecting diplomatic missions in the country.
Iraq has been roiled by over four months of demonstrations criticizing alleged government corruption, high unemployment and Iranian influence in Iraqi politics. Security forces have killed at least 500 protesters. The country is also facing a political clash over naming the next prime minister.
The latest protester's death came amid a violent pre-dawn crackdown by security forces on a protest camp in the southern city of Nasiriyah, an activist and a medical official said. The official spoke on condition of anonymity in line with regulations.
Police fired live rounds to disperse crowds from a central square in Nasiriyah where protesters were staging a sit-in, prompting demonstrators to flee. The encampment site was later burned. It was not immediately clear whether security forces or unknown groups had torched it. The city has been a frequent flashpoint in the protest movement.