Videos being shared on social media show the white flag fluttering above the Spin Boldak crossing near Kandahar.
Afghan officials have denied the post has fallen, although pictures on social media show the militants chatting to Pakistani border guards.
The BBC has been told the Taliban took the border crossing with no resistance.
In recent weeks, the militants have made rapid advances across the country, seizing a series of border posts from Afghan forces, including crossings with Iran, Tajikistan and Turkmenistan.