Abdul Hakim Taniwal was driving from his office when the attacker, his body strapped with explosives, ran towards the car and detonated the bomb, said Abdul Annan Raufi, the local police chief.
The other fatalities included one of Taniwal's bodyguards and another man, reportedly his nephew. At least three more people were wounded.
Taniwal, in his 60s, was a former sociology professor who had been in exile for about 20 years in Melbourne, Australia. He returned to Afghanistan following the fall of the Taliban government in late 2001.
He also served as minister in the government of Hamid Karzai, the Afghan president, and as governor of Khost province next to Paktia.
Paktia and other parts of eastern and southern Afghanistan - areas which run along the border with Pakistan - have suffered the worst of Taliban-linked violence.
Afghan officials allege much of the unrest is plotted by Taliban and al-Qaeda members who fled to Pakistan when the Taliban government was ousted.
On Friday, a car bomber rammed into a US military convoy near the US embassy, killing 17 people.