The ministry said in a statement the improvised explosive devices and roadside bombs were discovered in Paniwai district, in the southern part of the province, the Afghanistan Times reported.
The ministry also said several Taliban militants were killed and wounded in an army operation in Kandahar's Maiwand district. The army also inflicted several casualties during a cleanup sweep in eastern Ghazni province.
Two Afghan soldiers died in separate IED blasts in southern Zabul and neighboring Helmand province, the ministry said.
The Los Angeles Times reported two NATO troops were killed in separate engagements in southern and eastern Afghanistan. The newspaper said both soldiers died when they came under direct-fire attacks by enemy forces.
The U.S.-led International Security Assistance Force didn't provide details of the clashes or nationalities of the two soldiers killed, the Times said.
The Taliban claimed to have killed two U.S. soldiers in Laghman province, but a provincial government spokesman could not confirm the deaths, the Times said.
iCasualties.org, which tracks the NATO forces casualties in Afghanistan, said 158 coalition troops, including 126 Americans, have been killed in Afghanistan this year, down from 402 in 2012.
ISAF officials said they were still investigating last week's deaths of six U.S. service members whose Blackhawk helicopter crashed in Zabul province. Coalition officials said there were no reports of enemy activity at the time of the crash.