But Afghanistan's opium crop rose to 4,600 tonnes from 2,100 tonnes in previous years, leading to doubts about the implementation of the ban.
A decree from the supreme Taleban ruler, Mullah Mohammad Omar, broadcast on state radio, said anyone violating the ban would be severely punished.
"Anyone resorting to cultivating will be punished by the Islamic Emirate and their farming destroyed," the order said.
Mullah Omar said that poppy grown in Taleban-controlled area would be completely destroyed.
Leading producer
Last year, the Taleban leader ordered that cultivation be cut by a third.
But Afghanistan's opium crop rose to 4,600 tonnes from 2,100 tonnes in previous years, leading to doubts about the implementation of the ban.
A United Nations Security Council resolution raised concern over what it called the "significant rise in the illicit production of opium in Afghanistan".
In the poverty-stricken country, cultivating the opium poppy is lucrative - it needs less water than wheat and there is a steady supply route to Western markets via Pakistan.
The Taleban's strict version of Islam forbids the use of drugs.
But they say farmers must be helped to develop alternative crops before the cultivation of opium can be eradicated.
Help
Mullah Omar has also said Afghanistan needs help to eliminate poppy growth.
"As we have only limited means to utilise towards this end, we consider it the responsibility of the international community to assist us in this matter," he is quoted as saying by Reuters.
Correspondents say taxes on poppies have provided the Taleban with large sums of money, but in recent months they have begun enforcing a reduction in the amount grown.
Afghanistan has surpassed Burma, previously the world's largest producer of opium, and accounts for 75% of the world's total output.
However, a severe drought which has swept the country has threatened this year's crop.