The bombers, wearing explosive belts and disguised in military uniform, crossed security checkpoints and came close to the mausoleum of Saiyd Mohammed in Balad town, some 80 km north of Baghdad, Xinhua news agency reported.
At least one of the terrorists detonated his explosives belt at the marketplace outside the shrine and another at one of its gates, Xinhua said.
Also, two mortar rounds landed at the site at the time of the blasts.
The third bomber threw two grenades at a crowd of Shia pilgrims before he blew up himself among them, Xinhua quoted sources as saying.
More than 70 people were injured in the attack and some of the injured were in critical condition.
The suicide bombers were believed to be members of the Islamic State group.
Earlier reports said they took an unknown number of Shia pilgrims hostage but officials denied this, saying some people were caught inside the shrine.
The IS has claimed responsibility for the attack, saying three of its suicide bombers, including a female, attacked the shrine and killed dozens of Shias.
The online statement could not be independently verified.
The revered Imam Saiyd Mohammed is the son of Imam Ali al-Hadi and the brother of Hasan al-Askari, the 10th and 11th of the 12 most revered Shia Imams.
The Imam died in the ninth century and his tomb lies in the domed shrine constructed in Balad.
Iraq is currently witnessing a wave of violence since the IS terrorist group took control of parts of Iraq’s northern and western regions in June 2014.
The death toll from Sunday’s suicide bombing blamed on the IS at a marketplace in Iraq’s capital Baghdad has risen to 292, the government said on Thursday.
The government has handed over 115 bodies to their families and identities of 177 people are yet to be determined, Health Minister Adila Hammoud said.
A report by UN Assistance Mission for Iraq estimated that 662 Iraqis were killed and 1,457 wounded in acts of terrorism, violence and armed conflict in June across Iraq.