At least 50 people were wounded in the blasts, the officials said.
In the first attack, a suicide bomber detonated his explosive belt inside a restaurant in the Shi’ite neighborhood of New Baghdad, leaving 22 dead, police told Reuters.
In the second attack, two bombs ripped through the bustling Sharqa market district, killing 10 people.
In a third attack, a bomb killed two and wounded another seven in the Shi’ite section of Abu Sheir in Baghdad’s Dura neighborhood, police said.
The interior ministry spokesman Brigadier General Saad Maan said he did not believe the blasts were linked to the decision to lift the curfew.
The Iraqi government announced on Thursday that the decade-old curfew in the capital would end on Saturday at midnight and that four neighborhoods would be “demilitarized”.
The moves are part of a campaign to normalize life in Iraq’s war-blighted capital and to persuade residents that Baghdad no longer faces a threat from Islamic State, the militant group which seized large areas of northern and western Iraq last year.
Some form of curfew has been in place since the U.S.-led invasion to topple Saddam Hussein in 2003, hindering commercial and civilian movement. The midnight (1600 ET) to 5 a.m. (2100 ET) curfew has been in place for more than seven years.