The directive, issued on Sunday, is the latest curb on women's rights since the Islamist group seized power in August.
The majority of secondary schools remains shut for girls, while most women have been banned from working.
Campaign group Human Rights Watch said the new restriction moved further towards making women prisoners.
Heather Barr, the group's associate director of women's rights, told AFP news agency the order "shuts off opportunities for [women] to be able to move about freely" or "to be able to flee if they are facing violence in the home".
The latest directive, issued by the Taliban's Ministry of Promotion of Virtue and Prevention of Vice, said women travelling for more than 45 miles (72km) should be accompanied by a close male family member.
The document calls on vehicle owners to refuse rides to women not wearing Islamic face coverings, or hijabs, although it does not say which type of covering to use. Most Afghan women already wear headscarves.
It also bans the playing of music in vehicles.
Since taking power following the departure of US and allied forces, the Taliban have told most female workers to stay at home while secondary schools are open only to boys and male teachers.
The Taliban say the restrictions are "temporary" and only in place to ensure all workplaces and learning environments are "safe" for women and girls. During their previous rule in the 1990s, women were barred from education and the workplace.
Last month, the group banned women from appearing in television dramas and ordered female journalists and presenters to wear headscarves on screen.
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