The executed man was convicted of killing another man five years ago and stealing his motorbike and mobile phone.
According to reports, the man was shot dead by the victim's father with an automatic rifle.
The decision to carry out the sentence was made "very carefully" after the approval of three of the country's highest courts and Taliban leader Haibatullah Akhunzada, according to Zabihullah Mujahid, a Taliban spokesman.
The execution comes after the Taliban leader last month ordered judges to fully enforce sections of Islamic law that include public executions.