Diplomats based in the Baghdad neighbourhood said they could hear sirens blaring for around an hour after the attack.
The assassination of a high-profile researcher in broad daylight in Baghdad may prove to be a covert message for Washington.
No group has as of yet claimed responsibility for the rocket attack and no casualties have been reported.
The US killed the militia's commander Abu Mahdi al Muhandis along with the most influential Iranian commander Qasem Solaimani following militia's siege of the US consulate in Baghdad.
The deaths bring to nearly 250 the overall number of people killed this month in Iraq as security forces crackdown on the growing protest movement.
The US embassy in Baghdad and its consulate in the Iraqi Kurdish regional capital Erbil evacuated non-emergency staff this week.
In a government effort to symbolise peace a year after Daesh was defeated in Mosul, the walls of the highly secure Green Zone are slowly being knocked down. Here are the key challenges that persist in post-Daesh Iraq.
Iraq celebrated the one-year anniversary of the official defeat of Daesh. The anniversary also saw the partial re-opening of the 'Green Zone' in Baghdad to civilians 15 years after it was set up in the wake of the US-led invasion and occupation.
The Green Zone houses parliament, government buildings and many foreign embassies.
Iraqi Prime Minister Haider al Abadi calls for the arrest of protesters loyal to Shiite Muslim cleric Moqtada al Sadr who stormed the Green Zone in Baghdad on Saturday.
Hundreds of followers of Shiite cleric Sadr storm Baghdad's Green Zone and enter parliament building, protesting government's failure to reform
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