The hardline Islamists do not mind cricket, however, and the game is popular among many fighters. They have also promised to enforce a less strict version of Islamic law this time, after seizing the capital Kabul last month.
The Test match, to be played in Hobart from 27 November to 1 December, was scheduled for last year but was put off due to the Covid-19 pandemic and international travel restrictions. It will be Afghanistan's first Test in Australia.
Before the Australia tour, the Afghanistan team will feature in the Twenty20 World Cup, to be held in the United Arab Emirates from 17 October to 15 November.
Shinwari also confirmed Afghanistan's Under-19 cricket team will tour Bangladesh for a bi-lateral later this month.
Since the evacuation of the US and NATO forces from Afghanistan after the Taliban swept into Kabul last month there were fears that cricket and other sports would be hit.
But ACB officials categorically said that cricket was supported by the Taliban. Afghanistan's home ODI series against Pakistan -- shifted to Sri Lanka -- was however cancelled until next year over logistical and Covid-19 issues last week.