The bomb, detonated by remote control, was aimed at shoppers in the city’s Mureydi market, an Iraqi interior ministry source said.
The densely-populated and impoverished area is often targeted by Sunni fighters and police said the number of casualties could rise.
The Iraqi prime minister, Nuri al-Maliki, ordered the US and Iraqi military to lift a blockade of the district on Tuesday.
The blockade was imposed after a US soldier of Iraqi descent was believed to have been seized by the Mahdi Army, a Shia militia that controls the area.
The US military identified the soldier for the first time on Thursday, saying he was 41-year-old Ahmed Qusai al-Taayie.
Major general William Caldwell also confirmed reports that the reserve soldier was visiting his Iraqi wife when he was handcuffed and taken away by gunmen during a visit to the woman’s family.
Caldwell said that the soldier and his wife were “married in February 2005 and he didn’t arrive in theatre until November 2005”.
“So he has every right, of course, as an American soldier to marry whomever he wants… At the time he was abducted his wife was … here, in Baghdad.”
The spokesman said the US believed the soldier was still in the custody of his abductors and there was “an ongoing dialogue” to secure his release, although he did not say with whom the US was negotiating.
The military spokesman also said that sectarian killing in Baghdad dropped by 41 per cent last week during the US imposition of blockades on two Baghdad districts and the end of Ramadan, the Islamic month of fasting.