The blast damaged about 30 shops in central Tikrit and pools of blood were seen in the street.
Police swarmed the area, firing shots in the air.
Tikrit, which is located about 150km north of the Iraqi capital, Baghdad, is the capital of Salahuddin province and hometown of Saddam Hussein, Iraq's former president.
Overall violence has dropped sharply in Iraq since the worst days of the sectarian conflict in 2006-07 but bombings and shootings are still regular, often targeting police and government workers.
Hundreds of people have been killed since an inconclusive March 7 parliamentary election that has yet to produce a new government.