Police and army officers said the attack, which began on Tuesday night, also wounded at least 42 people.
A police lieutenant colonel said three militants shot dead three policemen in central Tikrit and then opened fire on civilians, before later blowing themselves up inside homes in the area.
Daesh issued a statement claiming the attack, saying it was carried out by seven militants who clashed with security forces until they ran out of ammunition and then detonated explosive belts.
Daesh seized Tikrit during a lightning offensive that overran large areas north and west of Baghdad in the summer of 2014, but Iraqi forces recaptured it the following year.
Iraqi forces are now battling to retake west Mosul — the country’s last city in which the terrorists hold significant ground.
But the militants still hold other areas in western Iraq and eastern Syria, and they will be able to carry out deadly bombings even if all areas under their control are recaptured.