Fighters in Sunni armed groups say they have not received wages from the government.
Police and hospital sources said at least two people were hurt in the blast, which caused a whole building to collapse.
At least one woman and a child were among the dead.
Abdul Rahman Mustafa, the governor of Kirkuk province, said: “What are these children and women guilty of that they should be targeted? The aim of such terror attacks is to ignite strife in Kirkuk.”
Arabs, Turkmen and Kurds are competing for power in the oil-rich city of Kirkuk, 290km north of the capital, Baghdad.
The majority Kurds want to incorporate the area into their autonomous northern region, while other groups want it to remain under central government control.