The Imam Ali shrine has been damaged in fighting between US forces and supporters of rebel cleric Moqtada al-Sadr in the holy city of Najaf.
One of the entrances to the shrine, the holiest Shia site in Iraq, was damaged in the attack on Tuesday, a development likely to spark outrage among Iraq's Shia majority.
It was not clear who fired the missiles. US forces have been fighting Shia militiamen loyal to rebel cleric Moqtada al-Sadr in Najaf and other Shia areas.
Ahmad Shebani, Sadr's representative at the shrine, said five or six missiles had hit the building. There was no immediate comment from US troops.
Witnesses said three people had been wounded in the attack, none seriously.
Sadr visited the shrine after the attack to personally inspect the damage, as crowds of supporters chanted.
Earlier this month, the vast gilded dome of the shrine was damaged in fighting. The US military and Sadr's militiamen blamed each other for causing the damage.
