The car bomb exploded near a restaurant in Tal Afar centre. Minutes later, a man wearing an explosive vest blew himself up in a crowd of onlookers.
Tel Afar is not far from the Syrian border, just west of the city of Mosul.
Earlier, a car bomb reportedly killed two people and wounded seven in a western part of the capital, Baghdad.
There has been a rise in attacks in Iraq since US troops left in December, leaving more than 200 people dead.
The violence has come amid a marked deterioration in Iraq’s fragile political process, with the country’s most prominent Sunni Arab politician being sought by the authorities on terrorism charges.
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