The 10sq km zone is located on the west bank of the Tigris river that bisects Baghdad.
It houses the US and British embassies, the Iraqi government headquarters and thousands of American troops.
Fighters blamed
Last month, the US military blamed what it calls Iranian-backed armed Shia groups for a series of deadly rocket attacks in Baghdad.
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Those included one that struck Camp Victory, the main US military headquarters, and an Iraqi housing complex on the capital's southwestern outskirts on February 18, killing at least five people and wounding 16 more, including two US soldiers.
The US military said the assailants were among factions that had broken with Muqtada al-Sadr, the Shia leader and head of the Mahdi Army militia, and refused to follow his ceasefire order.
Iran denies allegations that it is stoking the violence.
US troop deaths
The Green Zone attack comes a day after the US military announced the deaths of four soldiers in Iraq, including three in a single roadside bombing in Baghdad.
A US soldier also died from injuries sustained during a gun battle on Friday.
Separately, in Baghdad's southern al-Amel neighbourhood, five Iraqis were injured during clashes between the Mahdi Army on the one hand and US and Iraqi forces on the other.
Iraqi police also reported the deaths of six Iraqis after a US Apache helicopter struck two checkpoints near the central city of Samarra. Two Iraqis were wounded during the attacks.
Abu Faruq, leader of an Awakening Council unit allied with US forces against al-Qaeda in Iraq, said the six Iraqis were members of his group who had been manning the checkpoints when they came under attack.