The blast near al-Haq Square also injured 21 people.The attack took place just before Friday prayers near the Al-Razzaq mosque.
The bomber wore an army uniform, police said.
In the predominantly Shiite town of Kut, south of Baghdad, a bomb set off in Al-Amil square at around 10:00 am (0700 GMT) killed one person and wounded 17 others.
Two militants also died in the northern town of Hawijah when the bomb they were trying to plant unexpectedly went off, officials said.
Meanwhile, five people were killed and 15 injured in separate attacks in the central city of Baquba, security forces said.
In the northern city of Kirkuk, two gunmen were killed when the bomb they tried to plant on the side of the road went off accidentally.
Iraq has seen a surge in violence since the start of the year, with the UN reporting more than 2,500 people killed from April through June, the highest such level since 2008.