"This event proves that cultivation and production of narcotics in Afghanistan is inseparably related to terrorist forces," the interior ministry said in a statement.
Afghanistan produced 93 per cent of the world's opium last year, which is then processed to make heroin and exported to the West.
According to UN drug experts, the illegal drugs business is pumping more than $3bn a year into the Afghan economy.
The Taliban are said to impose a 10 per cent tax on poppy farmers who produce the opium and also on the drug traffickers.
Other clashes took place in eastern and southern Afghanistan, where Taliban and other groups are waging an armed campaign against government and foreign forces.
US-led international forces clashed with fighters in the Qarabagh district of Ghazni province on Monday, leaving six Taliban dead and eight others wounded, Zia Wali, a spokesman for the provincial governor, said.
There were no casualties among the Afghan and foreign forces, Wali said.
In southwestern Nimroz province, US-led forces and Afghan troops killed several fighters on Monday during a clash in Khash Rod district, a multinational-force statement said on Tuesday.
The troops were targeting a fighter involved in the movement of weapons and fighters in the area, it said.
They detained 14 other suspected fighters during the raid.
In another incident, US and Afghan soldiers fought off co-ordinated attacks in eastern Afghanistan and called in air attacks that left a dozen fighters dead and a dozen more wounded, the US military said.
In another development, US marines have pushed into Afghanistan's southern province of Helmand in a major new operation to flush out Taliban fighters.
The Nato-led force described the operation on Tuesday as the most significant in months in the troubled area, which is littered with poppy fields and classified as Taliban territory.