They say the attack in the provincial capital, al-Houta, could have been worse, but that guards managed to shoot the attacker before he drove his explosives-laden vehicle inside the building.
The officials spoke on condition of anonymity because they aren't authorised to brief journalists.
Al-Qaida in the Arabian Peninsula, considered by Washington to be the group's most dangerous branch, has expanded its territory in the chaos of Yemen's civil war, and has strongholds in the area around al-Houta.