The death toll was still rising more than two hours after police said the bomber joined a crowd of about 100 recruits outside the police station in Saddam Hussein's hometown of Tikrit, some 80 miles north of Baghdad.
Loudspeakers from the city's mosques were calling on people to donate blood for the wounded.
One Tikrit policeman said at least two of the dead were police officers. A second police officer said a grenade that had not exploded was found near the scene.
The casualties were confirmed by Dr. Anas Abdul Khaliq of Tikrit hospital.
The group of recruits was the first to vie for 2,000 new police jobs that Iraq's Interior Ministry recently approved for the surrounding Salahuddin province, which is dominated by Sunni Muslims. They were waiting for interviews and medical checks as part of the application process, police said.
Both policemen spoke on condition of anonymity because they were not authorized to release the information.
Insurgents have long found recruitment centers a favorite target, taking advantage of lax security measures just outside protective barriers at police stations and the confusion caused by desperate jobseekers vying for work in a country with an unemployment rate as high as 30 percent.
The attack starkly displayed Iraqi forces' failure to plug even the most obvious holes in their security as the U.S. military prepares to withdraw from Iraq at the year's end.
A similar strike on a recruitment center in central Baghdad last August left 61 dead and 125 wounded in what was one of the deadliest attacks of the summer.