A Sunni Muslim group claimed responsibility for the attack late Saturday.
A message from the Sunna Supporters Group was posted on an Internet site. The statement accused Shiites of killing Sunnis and throwing their bodies in the streets after badly torturing them. It added that Sunni women under detention were being raped by Shiites.
The blast, which occurred about 10 a.m. when the market was packed with shoppers, devastated the stalls where food and clothes are peddled and sent up a plume of gray smoke. Flames shot out the windows of several scorched cars.
Ambulances rushed to the scene and carried the victims to hospitals, where men cradled crying babies as doctors applied bandages to the infants.
Rasoul Zaboun, an official from the Imam Ali Hospital in Sadr City, said 66 people were killed and 87 wounded.
Police Col. Hassan Jaloob also said 22 shops and stalls were destroyed, along with 14 vehicles.
As firefighters doused the wreckage, an angry crowd shouted their allegiance to radical Shiite cleric Moktada al-Sadr and denounced both Sunnis and the new government of Prime Minister Nuri al-Maliki, reports CBS News correspondent Lee Cowan.
Gunmen kidnapped a Sunni female member of parliament in a Shiite area of the capital. Lawmaker Tayseer al-Mashhadani was traveling from nearby Diyala province in a three-car convoy to attend a parliament session Sunday when her party was stopped by gunmen, officials said.
The Sunni speaker of parliament, Mahmoud al-Mashhadani, described the legislator's kidnapping as "a major development and a violation against the will of the Iraqi people." He called for her immediate release and urged security authorities to work for her release, saying they are responsible for her safety.
The Iraqi Islamic Party, the largest Sunni political group, also condemned the kidnapping and said it holds the defense and interior ministers responsible for the ongoing violence in the capital.
Al-Mashhadani and seven of her eight guards were kidnapped by some 30 gunmen in civilian uniforms, the party said in a statement. It also said some of the gunmen were carrying pistols used by authorities, an apparent reference to Shiite militias believed to be working under the Interior Ministry.
Hamdi Hassoun, an official with the Iraqi Islamic Party branch in Diyala, said Mashhadani was stopped at a checkpoint manned by about 10 armed men in civilian clothes. After checking her identity card, the gunmen asked her and her bodyguards to step out, then forced them into other cars and drove them away, Hassoun said, adding that one bodyguard managed to escape.
Mashhadani is a member of the Iraqi Islamic Party, which is part of the Iraqi Accordance Front, a Sunni bloc that holds 44 seats in the 275-member parliament.
Mahmoud Othman, a Kurdish lawmaker, blamed the kidnapping on sectarian tensions, which threaten to plunge the country into civil war.
The violence came after a relatively calm day in Baghdad amid a four-hour driving ban aimed at preventing suicide bombs during Friday prayers. It underscored the difficulties faced by Prime Minister Nouri al-Maliki as he tries to curb rampant sectarian and ethnic attacks with strict security measures and a 24-point national reconciliation plan.
Al-Maliki, meanwhile, left for a whirlwind trip to Saudi Arabia, Kuwait and the United Arab Emirates to seek support for his national reconciliation initiative, which includes an amnesty for the mostly Sunni insurgents.
The prime minister was expected to brief the Sunni leadership of those three countries on his efforts to deal with the divisions between Shiites and Sunnis. Iraq's neighbors in the Persian Gulf fear sectarian tensions will spill over into their countries, which are dominated by Sunnis but have large Shiite minorities.