Police patrolling the route to that ceremony also came under attack, when a bicycle loaded with explosives detonated near a patrol car, killing two officers.
One of the bombings took place near a police patrol in southern Baghdad, killing three people, including a policeman and two civilians.
Another bombing took place Sunday night, in a shopping district in the Azamiyah neighborhood of northern Baghdad.
The bombing caused heavy damage to several shops and caused a fire in one building.
One eyewitness said he thought the blast had been caused by an improvised explosive device.
Meanwhile, thousands of Iraqi Shi?ites continued their pilgrimage to the holy city of Karbala Monday to commemorate Arbain.
The festival mourns the 7th Century death of Imam Hussein, the grandson of the prophet Mohammed
Security has been stepped up in the area, because of violence targeting Shi'ite pilgrims the past two years.
Despite Monday's violence, pilgrims said they would not allow threats to deter them from their journey.