The direction, which was issued on Sunday, was the latest sidewalk about women's rights because the Islamic group seized power in August.
The majority of high schools remain closed for girls, while most women have been banned from work.The Human Rights Watch campaign group said new restrictions moved further towards making prisoners.
Heather Barr, Director of the Female Group Partner, told the AFP news agency order "turn off opportunities for [women] to be able to move freely" or "to be able to escape if they face violence at home".
The latest direction, which was issued by the Ministry of Common Promotion and Prevention of Taliban's virtue, said that women traveling more than 45 miles (72km) must be accompanied by a member of a close male family.
Documents call for vehicle owners to reject the vehicle to women who do not wear the head of Islam or face cover, even though it does not say which type of cover is used. Most Afghan women have been wearing a headscarf.
It also prohibits playing music in the vehicle."I feel very bad," Fatima, a midwife who lives in Kabul, told the BBC, reacting to direction. "I can't go out independently. What should I do if my child or my child is sick and my husband is not available?"
He added: "Taliban catches our happiness from us ... I lost my independence and happiness."
Another Afghan woman told the BBC that, while the size would help some women "feel comfortable", family escort was not a guarantee of violence and harassment.
He referred to the incident at Paghman in 2015 when four women were kidnapped from their families in Gunpoint and were then raped.
"[Taliban] must create an environment around the country in such a way that women feel safe," he added.
Because of taking power after the departure of the US and allies, the Taliban had told the majority of female workers to stay at home while high school was only open for boys and men.
Taliban say that restrictions are "temporary" and only in place to ensure all workplaces and "safe" learning environments for women and girls. During their previous government in the 1990s, women were banned from education and workplaces.
