Confirming the incident, Rohul Amin, the provincial governor of Farah, said three of the wounded people were in critical condition in the provincial hospital.
Officials in both Kandahar and Farah blamed Taliban insurgents for the attacks.
Taliban militants, who ruled Afghanistan for five years before their government was toppled in a US-led military invasion, rely heavily on use of roadside bombs as part of their campaign against Afghan troops and more than 100,000 international soldiers, but most often civilians become the victims of such attacks.