"A refrigerator truck packed with explosives blew up inside Jamila market at around 6 a.m. " police officer Muhsin al-Saedi said. "Many people were killed and body parts were thrown on top of nearby buildings."
A statement circulated online by supporters of ISIS said the blast had targeted a stronghold of the Shi'ite Muslim militias.
The market in the Shiite neighborhood is one of the biggest in Baghdad selling wholesale food items.
Rescuers pulling bodies from the rubble stumbled over sheet metal that had formed the walls and roofs of vendors' stands.
People gathering at the scene cried and shouted the names of missing relatives; others cursed the government.
Security forces and militia groups are fighting ISIS in Anbar province, the sprawling Sunni heartland in western Iraq.
In Baghdad, Abadi has proposed sweeping reforms aimed at reducing corruption and patronage, the biggest changes to the political system since the end of U.S. military occupation.