Adil Zenaid Abideen, a police colonel, said: "Those killed included a woman and among the wounded are three children and five policemen. The police chief escaped the attack."
There has been an increasing number of attacks in and around Kirkuk, which is claimed by both Arabs and Kurds.
Long-standing Kurdish demands for incorporating Kirkuk into the northern Kurdish region of Iraq are to be put to a referendum before the end of the year, despite opposition from the city's other ethnic groups.
Also on Tuesday, the US military said that US and Iraqi forces had killed 23 alleged insurgents in a two-day battle against armed groups south of Ramadi.
The battle began on Saturday night after an armed group travelling in two trucks opened fire on a US position near Donkey Island on the Euphrates River in the western province of Anbar.
"Helicopters killed at least one insurgent and wounded another, and destroyed the two trucks, later determined to be loaded with weapons, ammunition and explosives," a military statement said.
Troops searching the area on Sunday morning discovered 22 dead insurgents, including seven wearing suicide vests, as well as 24 homemade grenades, 20 roadside bombs, and other weapons.
Clashes erupted again on Sunday afternoon.
In October last year Al-Qaeda in Iraq declared Ramadi to be the capital of an "Islamic State of Iraq", but the city is now largely in the hands of US-allied Iraqi forces after local tribal chiefs switched allegiances.