"The operation was successfully completed [on Sunday]," the statement said.
As a result of the raids, more than 16 tonnes of drugs, mostly opium, were reportedly seized in the southern region, which is the centre of a Taliban-led armed uprising and Afghanistan's biggest poppy-growing area.
Two factories for converting opium into heroin were destroyed and "a large number" of weapons and ammunition were seized in the raids, according to authorities.
Officials also said that joint forces managed to free 14 civilians being held by the smugglers and confiscated weapons, explosives and detonable vests during the operation.
Afghanistan is the world's largest heroin producer, with annual exports worth up to $3b.