Crowds of recruits were gathering outside the centre in western Baghdad's Nissur Square on Sunday morning when the bomber detonated explosives strapped to his body, a police spokesman said.
He said the toll was expected to rise as many of the injuries were serious.
Fighters regularly attack Iraq's fledgling security forces, often bombing recruitment drives as the government and US forces continue trying to boost their capability.
The attack was one of several in the capital on Sunday.
Just south of the city, police were searching for men who killed 10 Shia travellers and kidnapped about 50 others on Saturday night.
Earlier on Sunday, a pair of roadside bombings, directed against police patrols in Baghdad, killed at least six passers-by and wounded six others, said police spokesman Mohammed Abd al-Ghani.
Iraqi police commandos and US
soldiers secure the site
A car bomb outside a market in Baghdad's primarily Shia Karradah town centre killed at least one person and wounded five others, while a similar bomb killed two people and injured 13 in the mainly Sunni neighbourhood of Radhwaniyah, police said.
Unidentified attackers also shot dead police brigadier Abd al-Mutalib Hassan as he was leaving his Karradah home for work.
Five people were killed in drive-by shooting in different parts of Baqouba, 60km northeast of Baghdad.
The victims included a teacher, a taxi driver, a labourer, a truck driver and a phone company worker, provincial police said.
Patrols were looking for Sunni men who ambushed a convoy of minibuses at a fake checkpoint on a road near the town of Latifiyah, about 32km south of Baghdad in the so-called Triangle of Death on Saturday.
"We demand that the government take quick action to send troops there in order to know the fate of those kidnapped"
Abd al-Karim al-Anzi,
leading Shia politician
The men murdered 10 Shia passengers before taking the rest captives to an unknown location, said the spokesman.
A leading Shia politician said that local tribes had armed themselves and were headed to the area to join in the search, a step likely to set off more killings.
In an address to parliament, politician Abd al-Karim al-Anzi said the kidnappers had worn Iraqi army uniforms.
He said: "We demand that the government take quick action to send troops there in order to know the fate of those kidnapped."