Barbers in Kabul have received a similar order.
Penalties have been imposed for non-compliance with the order, the Taliban Islamic Police have said.
Already during its first rule, from 1996 to 2001, the Taliban enacted strict Islamic laws, including forcing men to grow beards.
However, since the fall of the previous Taliban regime, many men in Afghanistan have chosen not to wear their beards.
Barbers point out that the new order makes it very difficult for them to earn a living.