A political party formed by the tribal sheikhs, who led the challenge to al-Qaeda and other armed groups in the province, last week confirmed its domination of Anbar's local councils.
The party campaigned on a security platform in January's provincial elections.
No group immediately claimed responsibility for Thursday's attack
The blast followed an attack on a bus carrying police assigned to guard oil companies in Iraq's northern city of Kirkuk on Wednesday.
Ten people were killed in that explosion, which police said may have been caused by a parked car bomb or a car driven by suicide bomber.
Local officials blamed the attack on al-Qaeda in Iraq, which previously had a heavy presence in Anbar.
But the province turned into one of Iraq's quietest after Sunni tribesmen, paid by the US military, turned their guns on al-Qaeda in Iraq in late 2006.
Thursday's attack took the number of people killed in violence in Iraq so far this month to at least 99, with 297 wounded, according to an AFP news agency tally based on reports by police and security officials.