Taro Aso made the shock comments at a press conference in Utsunomiya, north of Tokyo.
He questioned whether police would be able to handle a mass influx of people fleeing war in North Korea, before making his extreme suggestion.
He said: “Can police handle them?
“Will the Self-Defence Forces be dispatched and shoot them down?
“We’d better think about it seriously.”
Mr Aso claied as many as 100,000 North Korean refugees could arrive along the Sea of Japan coast, and that some of them could be armed.
The question of if and where to take in refugees also needed to be discussed, he said.
Mr Aso added: “It’s a politician’s job to think of (emergency) response. It may not be an event in the distant future.”
The question of what would happen in the event of war toppling the Kim Jong-un regime has been raised many times before, and is one of the main reasons China is keen on calming tensions between Pyongyang and Washington.
Beijing, like Tokyo, fears a refugee crisis should the US eventually attack North Korea, and prioritises stability above denuclearisation.
But the rhetoric between US President Donald Trump and North Korean leader Kim Jong Un has become increasingly inflammatory, and stepped up a gear this week at the UN General Assembly in New York.
The President’s threat to “totally destroy” North Korea was met by an unprecedented personal address by Kim, who promised to “tame” Mr Trump “with fire”, calling him a “dotard”.
In responding to what he saw as the US President’s “insult” over his “rocket man” jibe, the Foreign Minister Ri Yong Ho said that it made “our rocket’s visit to the entire US mainland inevitable all the more.”