The strikes are the first successful hit on the embassy after numerous attempts in recent months.
There have been ongoing anti-American protests throughout Iraq.
The protesters are demanding that U.S. troops leave Iraq.
The attack marked a dangerous escalation in the spree of rocket attacks in recent months that have targeted the embassy or Iraqi military bases where American troops are deployed.
None of the attacks has been claimed but Washington has repeatedly blamed Iran-backed military factions in Iraq.
On Sunday, one rocket hit an embassy cafeteria at dinner time while two others landed nearby, a security source told AFP.
Only one injury is being reported at this time, but neither the U.S. embassy nor President Trump have commented on the attack.