Forty-two people were injured in the accident in Zheray in the province of Kandahar, police spokesman Matiullah Hilal told dpa, adding that the bus had been taking people to neighbouring Helmand province.
Women and children were among the injured and the number of dead may rise as some of the injured were in critical condition, Hilal added.
The driver had been driving recklessly and at high speed, according to Hilal.
The majority of road accidents in Afghanistan are caused by the narrowness and poor condition of the roads, a lack of traffic signs and reckless driving.
At least eight people were killed and four injured in a traffic incident in the Doshi district of Baghlan province in August.