Mohammad Yaquob, the acting Khost police chief, said: "Behind a wall, which was close to the meeting hall, was garbage in which explosives were detonated.
"The acting governor was slightly wounded on his foot due to broken glass, and the executive director and governor's office manager have been slightly hurt by flying glass, but they are fine.
"There was a big bang but the wall is still standing."
The attack came a day after Kai Eide, the outgoing UN special envoy to Afghanistan, said more emphasis needed to be put on a civilian rather than a military strategy in the fight to defeat the country's anti-government forces.
The blast came a week after a suicide bomber killed seven CIA employees and a Jordanian intelligence officer at a base in the province, where US-led forces have been fighting a Taliban-linked network based across the Pakistan border.
Al Jazeera sources said the man, identified as Hammam Khalil al-Balawi, had been brought to the base in the eastern Afghan province of Khost, by car, from across the border in Pakistan.