A car bomb claimed by Islamic State in a Shi'ite Muslim district of Baghdad has killed at least 50 people and wounded more than 60 others, Iraqi police and hospital sources said.

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.

Amaq news agency, which supports Islamic State, said a suicide bomber had targeted Shi'ite militia fighters.

The ultra-hardline Sunni jihadist group, which considers Shi'ites 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, mostly between the Shi'ite majority and the Sunni minority.

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.