Police said a man with an explosive vest had blown himself up as recruits were registering their names at the small Muthanna airfield, now used by the army in the Iraqi capital.
No group immediately claimed responsibility for the attack which occurred a day after Prime Minister Nouri al Maliki vowed to eradicate al Qaeda in Iraq.
In a televised address on Wednesday, he predicted victory as his army prepared to launch an offensive against Sunni Islamist militants who have taken over parts of the city of Falluja.
Fighters from the al Qaeda-affiliated Islamic State of Iraq and the Levant, which is also active across the border in Syria, overran police stations in Falluja and another city in Iraq's western Anbar province last week.
The government had asked last week for volunteers to join the military effort against al Qaeda.