A statement issued by the embassy on Wednesday said that "due to militia attacks at the US embassy compound, all public consular operations are suspended until further notice", reports Xinhua news agency.
"All future appointments are cancelled. US citizens are advised to not approach the embassy."
The US Consulate General in Erbil, the capital of Iraq's semi-autonomous region of Kurdistan, "is open for visa and American citizen services appointments", it added.
The statement came hours after the supporters of the Kataib Hezbollah (KH) militia group, a faction of Hashd Shaabi or the Iraqi Popular Mobilization Forces (PMF), who stormed the embassy withdrew from the perimeter of the embassy.
The protest started on Tuesday when hundreds of mourners, wearing Hashd Shaabi's military uniforms, rallied outside the embassy, chanting slogans against the December 29 US attack on KH bases in Iraq and Syria.
The protest then turned violent as the protesters managed to break into an outer yard of the embassy, but were repelled by the security forces who deployed tear gas against them.
Local media footage showed Qais al-Khazali, head of Asa'ib Ahl al-Haq militia, and top Hashd Shaabi leader Hadi Al Amri and Abu Mahdi al-Muhandis participating in the protest.
On December 29, the US forces bombarded headquarters of Hashd Shaabi's 45th and 46th Brigades, leaving 25 killed and 51 injured.
A US military statement said that it was in response to an attack last week on an Iraqi base near Kirkuk province that killed an American civilian contractor.
( With inputs from IANS )