The blast occurred just before 6 p.m. as the market was full of shoppers preparing for their evening meals. It set fire to about 20 shops and leveled a building, a security source told Reuters. Many vehicles were damaged by the blast, which also cut off electricity to the area.
A vendor who witnessed the blast told the Associated Press the car was parked near a two-story building with shops on the bottom floor and apartments on top. He said a nearby generator caught on fire, partially collapsing the building and burning several other houses.
Haider Fadhil, a 25-year-old metal worker, told the AP he was shopping with his two friends when the force of the blast tossed him through the air and knocked him out.
"When I regained consciousness, I found that my left hand and leg were broken," Fadhil said from his hospital bed. "Thanks be to God for saving me and thanks to those who carried me in their pickup truck to the hospital."
Baghdad had been relatively quiet since a May 10 truce ended weeks of fighting between Iraqi security forces and militants loyal to cleric Muqtada al-Sadr.
It was the deadliest car bombing since March 6, when a twin bombing killed 68 people in a crowded shopping district in the central Baghdad district of Karradah.
Tuesday's blast occurred on the same day the Iraqi parliament announced it will start holding sessions outside the U.S.-protected Green Zone in the fall -- the latest bid by Iraqi authorities to bolster public confidence and assert their independence.
In other violence Tuesday, an Iraqi state TV reporter was shot to death near his apartment in the northern city of Mosul, police said.
Muhieddin Abdul-Hamid, 50, was a local anchor for the station in Mosul, the center of an ongoing U.S.-Iraqi operation against the most prominent remaining stronghold of al-Qaida in Iraq.
A suicide bomber on a motorcycle also struck a Baghdad checkpoint manned by U.S.-allied fighters, killing one and wounding four, in the latest attack targeting Sunni groups that have turned against al-Qaida in Iraq.
Another suicide car bomber struck a police checkpoint in central Baqouba, northeast of Baghdad, killing one policeman and wounding 19 other people.