In a statement, the Islamic State group claims responsibility for the largest attack, which killed five people and wounded 22 in eastern Baghdad. It says a suicide bomber targeted Shiite pilgrims marking the holy month of Muharram.
Iraqi officials say two other attacks in southern Baghdad killed five people and wounded 15.
The Iraqi security and medical officials spoke on condition of anonymity as they are not authorized to brief the press.
The attacks come as Iraqi forces prepare to retake the city of Mosul from IS, the militant group's last urban stronghold in Iraq. IS has been carrying out attacks far from the front lines after suffering territorial losses.