One rocket hit the embassy cafeteria while two others landed a short distance away
At least three people were injured, security sources told Reuters. This would be the first time in years that staff have been hurt in such attacks.
No group has claimed responsibility but the US has blamed Iran-backed military factions in Iraq in the past.
Iraqi Prime Minister Adel Abdul Mahdi condemned the attack, stating that the continuation of such acts could “drag Iraq into becoming a battlefield”.
The US State Department said: “We call on the Government of Iraq to fulfil its obligations to protect our diplomatic facilities.”
Recent attacks have targeted the embassy or Iraqi military bases where American troops are deployed.
Iraq has been dragged into a rapid deterioration in relations between Iran and the US in recent months.
This included the US killing of the top Iranian military commander, Gen Qasem Soleimani, by a drone strike on 3 January at Baghdad airport.
Also assassinated in the US strike was Abu Mahdi al-Muhandis, an Iraqi who had commanded the Iranian-backed Kataib Hezbollah militia group.
Powerful Iraqi Shia cleric Moqtada al-Sadr has organised anti-American demonstrations aimed at pressuring US troops to leave Iraq.
Sadr’s supporters were involved in widespread anti-government protests before the cleric called for the focus to shift to the US after the killing of Soleimani.
They began withdrawing from anti-government sit-in camps on Saturday.