The attacker detonated his explosives outside the recruiting centre in the city's central Allawi neighbourhood as volunteers were waiting to register inside, according to a police official.
At least 25 people were wounded in the blast, he said.
A hospital official confirmed the casualty numbers. Both officials spoke on condition of anonymity because they were not authorised to talk to the media.
Its fighters last week overran parts of the key cities of Fallujah and Ramadi, both in Anbar province west of Baghdad, seizing control of police stations and military posts, freeing prisoners and setting up their own checkpoints.
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Iraqi troops, backed by pro-government Sunni militiamen, have since been clashing with the fighters and carrying out airstrikes against their positions in an effort to reassert control of the cities.
Tribal leaders in Fallujah, 65 kilometres west of Baghdad, have warned al-Qaeda fighters there to leave to avoid a military showdown.
It followed an attack late yesterday by gunmen who struck at army barracks in Diyala province, north of Baghdad, killing at least 12 soldiers.