Most have taken refuge in the provincial capital, Kandahar.
A program officer for the International Organization of Migration in Kandahar, Nasim Karim, told the AFP news agency that at least four villages have been evacuated from an area west of the city.
Karim said villagers have no other choice than fleeing. He said there are "threatened" if they don't support the Taliban; if they do they are being "bombed and shot at" by security forces.
The U.S.-led coalition says up to 80 Taliban were killed in air strikes in a village in Kandahar Province earlier this week. Afghan officials say the attack left at least 16 civilians dead, but Afghanistan's main human rights group says up to 30 may have died.