Kandahar Governor Muhammad Yusuf Pashtun was chairing a meeting at the headquarters of Spin Boldak district, near the Pakistani border, when a bomb attached to a motorbike went off in a parking area outside the compound, officials said.
An Afghan soldier and a young girl were killed and another soldier and a second civilian were wounded, they added.
They blamed "terrorists" for the attack, and said the target might have been Pashtun himself.
Authorities usually use the term "terrorists" to describe members of the ousted Taliban and their al-Qaida allies, blamed for a wave of violence across the country that has claimed more than 650 lives since August.
Kandahar used to be the main bastion of the Taliban and tribal rivalry and drug trafficking is rampant in the province.
Afghan President Hamid Karzai and former Kandahar governor Gul Agha Sherzai narrowly survived an assassination attempt in September 2002 when their vehicle came under fire from an unidentified assailant.