About 170 people were also wounded by the blast in Khan Bani Saad, a predominantly Shia town in Diyala province.
ISIL claimed the responsibility for the attack on Twitter and said the car was carrying around three tonnes of explosives. The group said Shias were the target.
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".
Iraq's speaker of parliament said the attack had struck an "ugly sectarian chord".
Salim al-Jabouri said the Sunni ISIL group seeks to destabilise the country by carrying out criminal acts and targeting innocent civilians.
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 'under pressure'
Reports from Baghdad, said the scale of the attack and the number of people killed had shocked many Iraqis.
"ISIL is under an enormous amount of pressure in Anbar province where the coalition has been using air strikes against them," A reporter told Bloom Gist.
"The authorities say what they are doing, as al-Qaeda did before them during its peak around 2006, 2007 and 2008, is attack another area when they come under pressure. They are saying, 'We still have the capacity to attack you'.
"This is a very tough fight for the Iraqis and they were expecting one but the size of this attack will concern many."
