Two more bombings struck later in the day in different parts of the Iraqi capital, wounding 10, police said.
The blasts are the latest in a string of attacks in the Iraqi capital, which was the scene last week of two devastating suicide truck bombings that targeted the foreign and finance ministries and killed about 100 people.
The body of al-Hakim, who died Wednesday in Tehran of lung cancer, was scheduled to be returned to Iraq on Friday.
The funeral procession was expected to start in Baghdad and make stops in several cities in Iraq's southern provinces before burial in the Shia holy city of Najaf.
Condolences were painted on black banners that hung from the main streets in Najaf, and hundreds gathered near al-Hakim's office and his family home to pay respects.
The government announced a three-day mourning period, beginning Thursday.
Al-Hakim, the leader of the Supreme Iraqi Islamic Council (SIIC), was one of Iraq's most powerful Shia parties and helped to establish an opposition movement in 1982 while in exile in Iran to fight the Sunni-dominated government of Saddam Hussein, Iraq's executed former leader.
He spent nearly two decades in Iran during Hussein's rule and returned after the US-led invasion of 2003.