Workers in the al-Rasheed market, one of Baghdad's largest co-operative produce markets, told the AFP news agency that a man parked a pick-up truck and walked away before it blew up.
Earlier reports suggested it had been a suicide attack.
Kamil Lahmoud, a Shia farmer from Mahmoudiya, said he had just sold his produce and was inside an office collecting his money when the blast happened.
"I was injured slightly in my head and left hand," he said. "I went out and saw many people covered with blood and bodies scattered everywhere."
The office of Major-General Qassim Moussawi, Baghdad's security spokesman, said that police had defused a second bomb in the same area.
The bombing follows an increase in attacks in Iraq as US forces prepare to leave the country's cities before a full withdrawal in 2011.
But despite the fact that April was the bloodiest month since last September, with 355 people killed, Iraq has insisted that the timetable for the pullout will not be altered.
"The Iraqi government is committed to the dates for the agreed-upon withdrawal of American forces from all the cities and towns by June 30 of this year," Ali al-Dabbagh, a government spokesman, said earlier this week.
US commanders and Iraqi leaders had previously hinted that troops might remain in some especially volatile areas beyond June.
Statistics compiled by the Iraqi defence, interior and health ministries showed that 290 civilians, 24 soldiers and 41 police officers died in attacks across the country in April, with another 747 people wounded.
The death toll was 40 per cent higher than in March.