"A refrigerator truck packed with explosives blew up inside Jamila market at around 6 a.m. (0300 GMT)," 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 Islamic State said the blast had targeted what it called a stronghold of the "charlatan army" and Shi'ite Muslim militias.
The market in the Shi'ite neighborhood is one of the biggest in Baghdad selling wholesale food items. A Reuters witness at the site saw fruit and vegetables mixed with shrapnel littering the blood-soaked blast crater.
Smoke rose from charcoaled debris. 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.
"We hold the government responsible, fully responsible," witness Ahmed Ali Ahmed said, calling on the authorities to dispatch the army and Shi'ite militias to man checkpoints in the capital.
Abadi took office last summer following the army's collapse in the face of Islamic State's takeover of the northern city of Mosul that left the Baghdad government dependent on militias, many funded and assisted by neighboring Iran, to defend the capital and recapture lost ground.
Security forces and militia groups are fighting Islamic State 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.