Samim Khpolwak, the governor's spokesman, says the explosion, which took place in Shah Wali Kot district early yesterday, also wounded four people.
No group has claimed responsibility for the attack.
Kandahar is regarded by the Taliban as their heartland. It had been largely peaceful for some years until a recent resurgence in insurgent violence.
In neighbouring Helmand province, police chief Noor Agha Kemtoz says the Taliban shadow governor, Abdul Manan, was killed by Afghan security forces in Marjah district late yesterday.