At least 37 people have been killed in three separate bomb attacks in Iraqi capital Baghdad.

In the first attack, a suicide bomber killed 22 and wounded at least 50 in an attack in the predominantly Shi'ite New Baghdad neighbourhood after detonating a suicide vest in a restaurant.

"The restaurant was full of young people, children and women when the suicide bomber blew himself up," witness Mohamed Saeed told AFP. "Many got killed."

There were more fatalities in attacks on markets in the centre and south-west of Baghdad.

Hospital officials confirmed the deaths to AFP.

The attacks came hours before a long-standing overnight curfew was set to be lifted.

Curfews have been in place since a US-led coalition toppled Iraqi president Saddam Hussein in 2003.

On Thursday, the Iraqi government announced that the curfew would be lifted at midnight on Saturday, and that four neighbourhoods would be demilitarised in order to normalise the capital, and reduce fears that the city is under threat from Islamic State, reports Reuters.

Interior ministry spokesman Brig Gen Saad Maan said he did not believe that the attacks were linked to the decision to lift the curfew.

No group has yet claimed responsibility for the attacks, but in the past both Islamic State and other militant Sunni groups have targeted Baghdad.