Parliament approves new version of law paving the way for elections early next year.
Many children were returning to school for the first time after the Muslim festival of Eid al-Adha.
Twenty-five children were among the wounded, two hospital officials said.
The officials spoke on condition of anonymity because they were not authorised to release the information.
The blast partially toppled a brick wall in front of the school, leaving a crater that quickly filled with muddy water, apparently from a broken water line.
The attack comes a day after the Iraqi parliament passed a new electoral law paving a way for the general elections in February.
Iraqi and US military officials have expressed concern about a possible spurt in attacks aimed at destabilising the government before next year’s elections.
On Monday, gunmen stormed a checkpoint near Tarmiyah, north of Baghdad, killing five members of an anti-al-Qaeda group, police said.
The men were members of the Sunni Awakening Council, one of many Sunni groups that have begun taking on al-Qaeda in Iraq.
There are an estimated 2.5 million Shia living in Sadr City, a stronghold of Shia leader, Muqtada al-Sadr, known for his anti-US stance.