Lieutenant Mohammed Khayoun said the car was parked along a street about 30 metres from a police checkpoint in a Shia part of the mostly Sunni neighbourhood of Dora.
Tuesday's blast left several cars burning and some nearby stores ablaze.
Another police officer, Major-General Mahdi al-Gharawi, said the bomb was detonated by remote control and an Iraqi suspected of triggering the device had been arrested.
Police First Lieutenant Maitham Abdul-Razaq said the explosion was apparently aimed at a police patrol but missed its target.
The wounded were taken to hospital, said Abdul-Razaq, who arrived at the scene shortly after the bomb went off at 4.45pm.
Terrified children screamed while several women wailed: "Our children have died" and "the terrorists, may God punish them."
Witnesses said at least four passing cars caught fire and some motorists were killed or seriously wounded in the blast. Ambulances hurried to the scene, while motorists helped ferry the wounded to hospitals.
The market consisted of shops selling primarily domestic appliances such as refrigerators and cookers. But vendors sell sweets and vegetables from sidewalk stalls. Shattered pieces of fruits and vegetables were scattered on the street, mixed with huge pools of blood.
Dora is among the most dangerous neighbourhoods in Baghdad, where car bombings and roadside bombs have been a daily occurrence since a Sunni-dominated anti-government campaign began in the summer of 2003.