No injuries were reported.
Foreign Ministry spokesman Ahmad al-Sahaf condemned the attack, and said Iraq was committed to protecting all diplomatic missions in the country.
Caretaker Prime Minister Mustafa Al-Kadhimi has been unsuccessful in trying to bring the quarreling groups to a settlement.
Al-Sadr’s party declined to attend a meeting Al-Kadhimi held last week.
Despite the explosion, the Australian convoy was able to enter the Green Zone.
The followers al-Sadr and his political rivals, a coalition of Iran-backed Shiite groups called the Coordination Framework, have been at odds since after last year’s parliamentary elections.
His supporters in late July stormed the parliament and have held frequent protests there.
The firebrand clerics supporters have regularly protested, demanding the dissolution of parliament and early elections.
On Tuesday, Al-Sadr’s supporters pitched tents and protested outside the Supreme Judicial Council, accusing it of being politicised in favor of their Iran-backed allies.