The dead, apart from the bomber, were a man, a schoolmistress and two pupils, said the director general of Kirkuk General Hospital on Wednesday.
Most of the wounded, seven of whom were in critical condition, were children attending a school with both primary and secondary classes.
The target of the attack was the offices of the two main Kurdish factions - the Patriotic Union of Kurdistan and the Kurdistan Democratic Party.
An estimated 200kg of explosives was crammed into a Nissan pick-up which was completely destroyed, said a police chief.
The windows of the PUK's offices were blown in by the force of the blast, an AFP correspondent on the scene reported.
Five of the wounded were from the PUK, local commander Jalal Jowher said.
He accused Islamic fighters from either the Kurdish group Ansar al-Islam or al-Qaida of being behind "this cowardly act".
Ramadi car bomb
Meanwhile, a car bomb killed several people at the house of a leading tribal chief in Ramadi on Wednesday.
The attack at the house of Majid al-Ali Sulayman, shaikh of the al-Dulaim tribe, also left others injured, Aljazeera's correspondent said.
US forces are fiercely opposed in
No further details on the casualties were reported, as Iraqi police prevented people from entering the hospital where they were transferred.
US forces surrounded the site, imposing a curfew on the area.
Ramadi is in a part of the country where resistance to the US-led occupation is strongest.
Attacks on US soldiers and Iraqi targets seen as linked to the occupying forces are common.
US forces are planning to hand over security responsibilities in the town to Iraqi police early next year.
In another incident, two Iraqi children were killed and two were wounded when an explosion ripped through a classroom near Karbala, medical staff said on Thursday.
"One of the wounded suffered serious injuries. The children were 11 or 12," the director of Al-Hussein Hospital, Abbas Musa al-Tamimi, said.
Police said they had opened an inquiry into Wednesday's blast at Al-Abid school, two km west of the city.
It was not immediately clear whether the explosion was the result of a deliberate attack, or one of the children had brought an unexploded device into the school as a toy.