A human rights ministry report says 85,000 killed in violence between 2004 and 2008.
Several buildings were damaged and a number of cars were reported to be on fire.
Police said at least 40 people have been wounded in the blasts.
The casualties have been confirmed by an official at the Karbala hospital.
Iraq has seen a dramatic drop in violence over the past 18 months since the US committed thousands of extra troops to shore up its efforts in the country, but attacks are still common.