Crowds went on a rampage of grief and anger after the explosion, smashing the windows of cars parked in the street. Body parts were flung onto the roofs of nearby buildings by the force of the blast, police said.
"Some people were using vegetable boxes to collect children's body parts," police Major Amed al-Tamimi said from the site of the explosion, describing the damage to the market as "devastating."
An officer from the Diyala police command said rescue crews were still retrieving bodies from under the debris so the death toll could rise.
The Diyala provincial government declared three days' mourning and ordered all parks and entertainment places to close for the rest of the Eid al-Fitr holiday to pre-empt any further attacks.
ISIL said in a statement issued on Twitter that the attack was to avenge the killing of Sunni Muslims in the northern Iraqi town of Hawija, and that the suicide car bomber was carrying about three tons of explosives.
Iraqi officials declared victory over ISIL in Diyala earlier this year after security forces and Shia paramilitaries drove them out of towns and villages there, but the insurgents remain active in the province.
Security forces and militia groups are currently focused on the western province of Anbar, where they have been gearing up for an offensive to retake the mainly Sunni governorate — Iraq's largest.
The United Nations said earlier this week that nearly 15,000 people had been killed in the 16-month period up to April 30.