Speaking in an interview with the BBC, Mateusz Morawiecki said that recent events showed the Kremlin and allies wanted to "change the geopolitical system" and "disunite" the European Union.
He cited a build-up of Russian forces near Ukraine, soaring gas prices and a crisis on Poland's border with Belarus, the British public broadcaster said on its website.
His comments came ahead of a two-day meeting of NATO foreign ministers in Riga, Latvia.
NATO and EU leaders have recently accused Belarus of orchestrating a migrant crisis on its border with Poland.
Speaking to the BBC's Europe Editor Katya Adler, Morawiecki said it was "not too late to act" but it could be several months from now.
"Bad things may happen in Ukraine for instance, or there could be another huge migration problem for the whole of Europe," he said in the interview, which was aired by the BBC on Tuesday.
Morawiecki said he believed the "immediate perpetrator" behind the border crisis was Belarusian leader Alexander Lukashenko. But "he has his sponsor, he has his principal" in the Kremlin, Morawiecki added, referring to Russian President Vladimir Putin.
"All the pieces of the puzzle put together present not a very good picture," he concluded.