At least 100 other people were injured in the blast in the town, some 80 miles (130 km) north of Baghdad.
The toll from Tuesday morning’s blast was the highest from a single attack since a Baghdad church siege in October which killed more than 50 people.
Violence in Iraq has ebbed in recent years, but deadly attacks persist.
The bomber – wearing a vest packed with explosives – was in the middle of about 100 volunteers who were waiting outside the building to be interviewed, witnesses said.
Most of his victims were police recruits, officials say.
Ahmed Abdul-Jabbar, deputy governor of Salahuddin province, said the attack was the work of “terrorists”.
“Who else would it be but al Qaeda, who keep on slaughtering us?” he said.
Tikrit’s main hospital has been inundated with casualties, reports say, and local mosques have been broadcasting appeals for residents to donate blood.
The death toll is unusually high for a suicide bombing carried out by one man operating on foot, analysts say. Some estimate the bomber may have been carrying as much as 50kg of explosives.