He said the blast damaged the shops and sparked a fire in three vehicles.
Kirkuk is the capital of the oil-rich province of the same name which is disputed by the federal government in Baghdad and the autonomous region of Kurdistan.
The blast comes as Kurdish leaders prepare to hold an independence referendum on September 25 in the face of fierce opposition from Baghdad and the Kurds' international backers.
The Kurdish Regional Government is embroiled in long- standing disputes with the federal government over oil exports, budget payments and control of ethnically divided areas.
Kirkuk, which is home to diverse communities including Arabs and Turkmen who oppose the vote, is under the authority of the Baghdad federal government.