Police officials said gunmen in two speeding cars opened fire on the stores in the northern neighborhood of Waziriyah, killing nine people and wounding four others.
Islamic extremists have frequently targeted liquor stores in Iraq, but alcohol remains available in most cities.
Also, a bomb went off this afternoon at an outdoor market in the northern city of Mosul, killing two shoppers and wounding 15 others.
One hour later, police said, two people were killed and seven others were wounded when a roadside bomb exploded on a road frequently used by military convoys in Mishahda village, just north of the capital.
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Police said a friend of the son was killed also in the attack.
The militia, known as the Sahwa, had joined forces with US troops at the height of the Iraq war to fight al-Qaida. Ever since then, it has been a target for Sunni insurgents, who call its members traitors.
Medical officials confirmed the casualty figures. All officials spoke on condition of anonymity because they are not authorised to speak to media.