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 Shiite holy city of Najaf, Iraqi Vice President Vice President Adel Abdul-Mahdi told AP Television News.
The government announced a three-day mourning period, beginning Thursday.
The deadliest bombing Thursday struck at about 11 a.m. near a U.S. military base close to Taji, north of Baghdad, killing one and wounding six people, an Iraqi police official said.
Hours earlier, three bombs attached to three parked cars exploded nearly simultaneously in Baghdad's primarily Sunni neighborhood of Azamiyah, wounding four police officers and two civilians, said another police official.
Two more bombings struck later in the day in different parts of the Iraqi capital, wounding 10, police said.
All the officials spoke on condition of anonymity because they were not authorized to release the information to the media.
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 U.S. military is closely watching the developments around al-Hakim's death, including how it could impact Iraq's political landscape.
The military has expressed concerns about spikes in violence ahead of January's parliament elections.
"With or without al-Hakim's death, that is always the possibility as we move closer to the elections," said Brig. Gen. Stephen Lanza, a U.S. military spokesman. "There is political posturing that potentially could lead to violence."
Al-Hakim's political bloc, the Supreme Islamic Iraqi Council, became the most influential Shiite political force following Saddam Hussein's collapse, working with American forces in Iraq while keeping its ties to Iran as the Islamic regime expanded its influence with Iraq's Shiite majority.
Though al-Hakim had been grooming his son to take control of the party, it remains unclear if the heir could hold it together.
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. Meanwhile, hundreds began arriving in Najaf from other provinces in preparation of the funeral.
Meanwhile, the trial resumed Thursday for five members of Iraq's security forces charged in a deadly bank heist. A judge had adjourned the proceedings earlier this week, after relatives of slain bank guards beat and spat on the defendants.
Gunmen broke into the state-run Rafidain Bank at about 4 a.m. on July 28, killing eight guards. Most of the money was later recovered in the office of a newspaper owned by Abdul-Mahdi, the Iraqi vice president, investigators said.
Two of the defendants told the court Thursday they were tortured into making false confessions, while two others said they were approached about the robbery but did not participate. A fifth defendant, who worked at the newspaper, said he was arrested because he was related to one of four other suspects still wanted in the case.
Despite the drop in overall insurgent violence in Iraq, armed robberies have been on the rise.
Gunmen broke into the Baghdad office of Turkish Airlines and stole $160,000, said an Iraqi police official, who spoke on condition of anonymity for the same reason as the others.
The theft was discovered Thursday morning, the official said.
Associated Press Writers Sameer N. Yacoub and Bushra Juhi contributed to this report.