Four of the rockets landed inside the Green Zone, and three outside it.
The Green Zone is an area of Iraq's capital city where the embassies for the US and several other western countries are located. It is largely viewed as a safe location, but is frequently the target of rocket attacks.
A US official said US personnel moved into shelters during the incident. The US has yet to do a complete damage assessment, but initial findings indicate no injuries to US persons and no material damage to the embassy.
Iraqi security forces located the launch site of the rockets in Baghdad's eastern al-Ameen neighborhood, according to an Iraqi military statement.
The military released images of the launch site which displayed the rocket launcher outside on a street and on fire.
In the past, some rockets have been fired at the Green Zone to protest US troop presence in Iraq.
The deadly launches on Tuesday came just after the Trump administration announced that the US will withdraw thousands more US troops from Iraq and Afghanistan by Jan 15, 2021 -- days before President-elect Joe Biden takes office, confirming plans first reported by CNN on Monday.
The planned withdrawal will leave approximately 2,500 troops in both countries,