The SUV packed with explosives went off near a beauty salon in a bustling market at rush hour in Sadr City. Most of the victims were women and many of the wounded are in critical condition, the sources said.
Amaq news agency, which supports Islamic State, said a suicide bomber had targeted Shia militia fighters.
The ultra-hardline Sunni jihadist group, which considers Shias apostates, claimed a twin suicide bombing in Sadr City in February that killed 70 people.
Security has gradually improved in Baghdad, which was the target of daily bombings a decade ago, but violence directed against both the security forces and civilians is still frequent and large blasts sometimes set off reprisal attacks.
The fight against Islamic State has exacerbated a long-running sectarian conflict in Iraq.
Sectarian violence also threatens to undermine US-backed efforts to dislodge the militant group from vast areas of the north and west of Iraq that they seized in 2014.