Local officials said explosives detonated in a vehicle that drove into a market crowded with shoppers in Orgun district. They added that dozens more people, mostly women and children, were injured and hospitalized.
Police pursued the vehicle before it entered the market, eyewitnesses said.
The local Taliban announced it was not responsible for the incident, which occurred near Afghanistan's border with tribal areas of Pakistan, a place in which the Pakistan-based Haqqani militant network has a presence.
Local police commander Azizullah, credited with bringing a measure of security to the province, survived an assassination attempt in the area last week.
The bomb blast came hours after two members of outgoing President Hamid Karzai's media team were killed in Kabul, the capital, by a roadside bomb for which the local Taliban took responsibility.
Several days ago, Afghanistan's two presidential candidates, in the recently-concluded election, agreed to abide by a vote audit after allegations of vote fraud.