Qaderi headed the ministry since December 2004 and survived several cabinet shuffles, but Afghanistan's poppy crop has ballooned under his watch and the country's production last year accounted for more than 90 per cent of the world's heroin supply.
Western and UN officials have said this year's harvest could equal or exceed last year's record crop.
Khodaidad said Qaderi did a "wonderful job" in the north, where cultivation is expected to drop, but said there were "some problems" in the south, where violence has spiked this year.
Qaderi's resignation comes as US and Afghan officials debate privately whether to use herbicides to reduce the drug problem.
Karzai rejected that approach for the 2007 growing season partly because some Afghans fear the chemicals could affect livestock, legitimate crops and drinking water, fears the US says are unfounded.
Much of the profit from the country's $3.1 bn drug trade is believed to fund the Taliban fighting against the government.
Officials said on Sunday that recent clashes between police and fighters left 11 suspected Taliban members dead in the south, while Taliban fighters ambushed police in Kandahar province, wounding 15 officers.