A correspondent for the AFP news agency said a short funeral procession would be held soon.
Al-Hakim, 60, had fought the Iraqi government of Saddam Hussein, the executed president, and was praised by political leaders in both Iraq and Iran.
Mahmoud Ahmadinejad, the Iranian president, called al-Hakim's death "a great loss for the Iraqi people".
He paid particular tribute to al-Hakim's family, describing them as "revolutionaries", the official IRNA news agency reported on Wednesday.
In 1982, al-Hakim helped to establish an opposition movement in exile in Iran to battle Saddam's Sunni-dominated government, and returned to Iraq after the US-led invasion of 2003.
His SIIC party swept Shia areas in the first provincial elections after the invasion, but in elections this January it suffered major losses.