Tikrit police said the attacker set off his explosives-laden vest at a checkpoint where recruits wait to enter a recruiting center, causing a fire at a nearby fuel station, CNN reported.
Police said most of the dead and wounded were men who were interested in joining the Iraqi police.
Witnesses told the BBC the bomber was in the middle of a group of volunteers waiting outside to be interviewed.
Officials said the main hospital in Tikrit has been overcome with casualties and local mosques have been issuing appeals for blood donations.
Ahmed Abdul-Jabbar, deputy governor of Salahuddin province, blamed the attack on terrorists.
"Who else would it be but al-Qaida, who keep on slaughtering us?" he said.
No one has claimed responsibility, but al-Qaida in Iraq, the Sunni Muslim-dominated militant group, has frequently carried out such attacks, the report said.
Tikrit, 100 miles north of Baghdad, is largely a Sunni Muslim city.
It was the hometown of the late Iraqi leader Saddam Hussein, and the recruitment center is located in one of Hussein's former palaces.