Hamidzada would not say what the pair were alleged to have done.
One government official told AFP news agency: "They are British and were arrested five days ago."
Another senior official said: "They, with support from their Afghan colleagues, had done things contrary to their jobs and had posed a threat to the national security of Afghanistan."
The foreign nationals would be expelled and their Afghan colleagues would go through a judicial process, he said.
Afghanistan's foreign ministry confirmed there had been arrests but said it would not immediately release details.