A man sped up on a motorcycle to the office in the southern city of Dalea before stopping suddenly and blowing himself up, witnesses who were in a nearby market told Reuters by telephone.
A senior figure in the provincial government said the blast "bears the hallmarks of an Al-Qaeda attack," adding that eight soldiers were wounded.
Al Qaeda in Yemen previously focused high-impact strikes on foreign targets, but has started to target the state in response to enhanced US-Yemeni cooperation in a crackdown on the militant group that has included air strikes and raids.
Four other assaults on state targets have been blamed on Al-Qaeda's Yemen based regional arm since June, though it has only claimed two. The most recent attack by suspected militants killed six soldiers.
"You are covering for American crimes to subjugate the people of this country and to serve US interests in the region," said the audio recording, posted on an Islamist website on Thursday. "God willing, we will strike again when the time is right."
Yemen, struggling with rebels in the north and a rising separatist movement in the south, is under international pressure to quell domestic conflicts and focus on a resurgent Al-Qaeda in the country.
Western powers and neighboring top oil exporter Saudi Arabia fear the militant group is exploiting growing instability in Yemen to use it as a launch pad for attacks regionally and beyond.
The impoverished Arabian Peninsula state surged to the forefront of Western security concerns when Al-Qaeda's Yemen wing claimed responsibility for the botched bombing of a US-bound plane in December.
