Al-Hakeem's office announced on Friday that he died of a sudden medical condition it did not specify. A relative, Mohsen al-Hakeem, told The Associated Press news agency that al-Hakeem died at the Al Hayat hospital in Najaf where he was taken after suffering a sudden heart attack.
Funeral ceremonies will be held on Saturday in Najaf and its twin holy city of Karbala, a source within his office told AFP news agency.
Iraqi President Barham Salih in a statement paid homage to the "prominent figure" in Shia Islam.
Born in Najaf in 1936, al-Hakeem was considered to be among the highest Shia religious authorities in the country.
At the time of his death, he was one of four ayatollahs of the Hawza, Najaf's Shia seminary, along with Grand Ayatollah Ali al-Sistani, Iraq's top Shia spiritual leader.
Along with the Afghan-born Mohammed Ishaq al-Fayadh, al-Hakeem was seen as the most likely contenders to succeed al-Sistani.
His maternal grandfather was Mohsen Al-Tabataba'i Al-Hakeem, a scholar and one of the most prominent thinkers of Shia Islam. His father was Muhammad Ali al-Hakeem, one of the most respected Shia leaders in Najaf.
His second cousin, Sayyed Ammar al-Hakeem, leads the al-Hikma, or National Wisdom Movement, one of the largest Shia political parties in Iraq.
Al-Hakeem was imprisoned between 1983 and 1991 under the government of Saddam Hussein who feared neighbouring Iran's 1979 Islamic revolution would set off "a similar event" in Iraq, political commentator Marsin Alshamary said on Twitter.
Al-Hakeem has written many books and publications, some of which were translated into several languages. He is survived by a wife and eight children.