Anyone violating the rule will be punished, Taliban religious police say.
Some barbers in the capital Kabul have said they also received similar orders.
The instructions suggest a return to the strict rulings of the group's past tenure in power, despite promises of a milder form of government.
Since taking power last month, the Taliban have carried out harsh punishments on opponents. On Saturday, the group's fighters shot dead four alleged kidnappers and their bodies were hung in the streets of Herat province.
In a notice posted on salons in southern Helmand province, Taliban officers warned that hairdressers must follow Sharia law for haircuts and beards.
"No one has a right to complain," the notice, which was seen by the BBC, read.
"The fighters keep coming and ordering us to stop trimming beards," one barber in Kabul said. "One of them told me they can send undercover inspectors to catch us."
Another hairdresser, who runs one of the city's biggest salons, said he received a call from someone claiming to be a government official. They instructed him to "stop following American styles" and not to shave or trim anyone's beard.
During the Taliban's first stint in power from 1996 to 2001, the hardline Islamists banned flamboyant hairstyles and insisted that men grow beards.
But since then, clean-shaven looks have become popular and many Afghan men have gone to salons for fashionable cuts.
But the barbers, who have not been named to protect their safety, say the new rules are making it hard for them to make a living.
"For many years my salon was somewhere for young people to shave as their wish and look trendy," one told the BBC. "There is no point to continue this business."
"Fashion salons and barbers are becoming forbidden businesses," another said. "This was my job for 15 years and I don't think I can continue.
Another barber in the western city of Herat said that although he had not received an official order, he had stopped offering beard trims.
"Customers don't shave their beards [because] they don't want to be targeted by the Taliban fighters in the streets. They want to blend in and look like them."
Despite slashing his prices for a cut, his business has dried up. "Nobody cares about their style or hair fashion," he said.