The first blast, reportedly from a parked car bomb, exploded at 0730 (0330GMT) in a market in the northern oil city, killing at least 10 people, with several more blasts following in quick succession on Tuesday.
A second car bomb came 30 minutes after the first blast in front of the city's main police headquarters. The bomb, which killed two policemen, was aimed at police commander Major-General Turhan Yusuf, however he survived.
Three other bombs later exploded in the city. One was aimed at Colonel Tahir Salah al-Din, the police chief for southern Kirkuk's al-Hurriya neighbourhood, who survived, although one of his bodyguards was killed.
Kirkuk is a centre for oil production and home to an ethnic and sectarian mix of Kurds, Turkmen and Arabs.
The violence comes as authorities in the Iraqi capital, Baghdad, imposed a strict curfew on the city in an attempt to curb continuing violence.
Civilians and soldiers carried the
wounded to ambulances
The curfew will run from 9pm local time (1700 GMT) until 6am (0200 GMT), while vehicles will be banned from the city's roads on Fridays during prayer times, an interior ministry official said.
There will be a total ban on people carrying weapons in the city and more police forces would be mobilised on the streets, he added.
Also in Baghdad, the judge presiding over the trial of Saddam Hussein, the former president of Iraq, said Tuesday would be the final day for defence witnesses.
On Tuesday, Barzan al-Tikriti, Saddam Hussein's half-brother and co-defendant, was barred from court after being thrown out the day before for criticising the judge.
Saddam Hussein and seven others are on trial for crimes against humanity in relation to the deaths of 148 Shia villagers in Dujail in 1982.