Dozens of people were also wounded by the blast in Khan Bani Saad, approximately 30km northeast of the capital Baghdad.
ISIL claimed responsibility for the attack on Twitter and said the car was carrying around three tons of explosives, according to a report by Al Jazeera on Saturday.
Angry crowds went on the rampage after the explosion, smashing the windows of cars parked in the street in grief and anger.
"Some people were using vegetables boxes to collect body parts of kids' bodies," police major Ahmed al-Tamimi told the Reuters news agency from the site of the explosion, describing the damage to the market as "devastating".
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.