One of the entrances was damaged in the attack on Tuesday.
It was not clear who fired the missiles. US forces have been fighting Shia militiamen loyal to leader Muqtada al-Sadr in Najaf and other Shia majority areas.
Ahmad Shibani, al-Sadr’s representative at the shrine, said five or six missiles had hit the building.
Another spokesman for al-Sadr said it was US troops that fired an Iraqi-made mortar on the shrine.
“As you know US forces put their hands on weapons that belonged to the former Iraqi army, so it could have been a mortar from this arsenal that was fired at the shrine,” said Sheikh Qais al-Khazali.
He dismissed accusations that members of al-Sadr’s Mahdi army may have been responsible for the attack.
“It is impossible for Shias to do this,” said Khazali. “We control the shrine area. How can we fire a mortar on ourselves?”
However, US Brigadier General Mark Kimmitt said US forces were not responsible for damaging the mosque. “The coalition forces had no involvement in the damage to the Imam Ali mosque,” he told a news briefing in Baghdad.
Earlier this month, the vast gilded dome of the shrine was damaged in fighting. The US military and al-Sadr’s militiamen blamed each other for causing the damage.