Lt. Mohammed Khayoun said the car was parked on a street about 30 yards from a police checkpoint in a Shiite part of the mostly Sunni neighborhood of Dora.
The blast left several cars burning and some nearby stores ablaze.
Another police officer, Maj. Gen. Mahdi al-Gharawi, said the bomb was detonated by remote control and an Iraqi suspected of triggering the device had been arrested.
Police 1st Lt. Maitham Abdul-Razaq said the explosion apparently was aimed at a police patrol but missed its target.
The injured were taken to hospital, said Abdul-Razaq, who arrived at the scene shortly after the bomb went off at 4:45 p.m.
Dora is among the most dangerous neighborhoods in Baghdad, where car bombings and roadside bombs have been a daily occurrence since a Sunni-dominated insurgency began in the summer of 2003.
Terrified children screamed while several women wailed: "Our children have died" and "the terrorists, may God punish them."
In other developments:
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.
Amidst the on-going violence, Britain's foreign secretary told Iraqi leaders Tuesday they must form a national unity government free of domination by a single group, reinforcing U.S. pressure on political leaders to put aside ethnic and sectarian differences in the interest of the nation.
Foreign Secretary Jack Straw, who arrived in Baghdad late Monday, told reporters that the results of the Dec. 15 parliamentary election showed that the Iraqi people want a "broad government of national unity" to bring together "all the different elements" of Iraqi society.
"It is a crucial moment today for the people of Iraq," Straw told reporters alongside President Jalal Talabani. "The international community, particularly those of us who played a part in liberating Iraq, obviously have an interest in a prosperous and stable and democratic Iraq."
Straw said Iraqis want a government where "no party, no ethnic or religious grouping can dominate the government."
His comments came the day after U.S. Ambassador Zalmay Khalilzad delivered a blunt message warning that Iraqi leaders risk losing American support unless they establish a national unity government with the police and army out of the hands of religious parties.
The British foreign secretary's visit was a sign of international concern over the direction of talks among Iraq's Shiite, Sunni Arab and Kurdish political parties as they attempt to put together a government following the December elections.
Iraqis have until mid-May to form a new government, but U.S. and Iraqi officials warn the process could take longer because of political differences.
A coalition of Shiite religious parties won 130 of the 275 seats in the new parliament. Although they have agreed in principle to a unity government, Shiite leaders insist their strong showing in the election gives them the right to control key levers of power. A Kurdish alliance won 53 seats and two Sunni Arab blocs together took 55 seats — a major increase over Sunni representation in the outgoing parliament.
One key issue is control of the ministries of Defense, which runs the army, and Interior, which manages the police. Sunni Arabs have accused the Shiite-run Interior Ministry of widespread human rights abuses, including kidnappings and murder, a charge denied by the ministry.
In the latest example of sectarian killings, the spokesman for a political party that is part of a Sunni Arab bloc in the new parliament was found dead of multiple gunshot wounds, family and associates said Tuesday. Saad Jarallah of the National Dialogue Council did not return home from work Friday, according to relatives who found his body at the Baghdad morgue Monday.
After Jarallah's funeral Tuesday, the head of his party said talks were deadlocked.
"After this incident, there is no way for Iraqis but to protect themselves and confront every aggressor," Khalaf al-Ilyan said. "They should not expect protection from the government."
The United States, Britain and the other coalition members believe that a unity government is essential to their strategy of handing over security to Iraqi soldiers and police so that international troops can begin to go home this year.
In other attempts to resolve political divisions, Iraqi leaders plan a second reconciliation meeting in the first week of June, Arab League envoy Mustafa Othman said Tuesday after meeting with Foreign Ministry officials in Baghdad.
The conference will take place in Iraq under the auspices of the league, which is trying to assure Sunni Arab participation in a political process now dominated by the Shiite majority and large Kurdish minority, considered key to ending the insurgency.