Similar attacks near a crowded marketplace also left six people dead and more than two dozen others wounded near the city of Hilla south of the capital. Local sources said 11 schoolgirls also sustained injuries in a grenade attack near a secondary school in the city.
Over the past few months, hundreds of people have been killed in bombings and shooting attacks in Iraq.
Official figures show that September was the bloodiest month in Iraq in almost two years, with attacks killing over 360 people.
At least 21 people have been killed and scores of others injured in bomb attacks in Iraq, officials say.
The bombings were carried out on Wednesday morning in the capital, Baghdad, and three other cities, security and medical sources said.
Five people were killed and over 30 others injured in two car bomb attacks and a roadside bombing in Kirkuk, the capital of a province with the same name.
Four people were also killed and five others wounded in a bomb attack targeting an Iraqi army patrol in Kirkuk’s city of Hawijah.
In Baghdad, at least six people were killed and dozens of others injured in two car bombings. Police sources said an Iraqi major general survived one of the attacks that targeted the convoy transporting him.