Mariusz Kamiński made the statement on Twitter on Sunday, the state PAP news agency reported.
Russia has been massing troops and military hardware around Ukraine for weeks, fueling concerns among Western leaders that an invasion could be imminent.
Moscow has denied any such plans, but has demanded security guarantees from the United States and NATO. These include a ban on the alliance’s eastern expansion and a withdrawal of infrastructure from NATO’s eastern flank, PAP reported.
“Given the situation in Ukraine, we are obviously preparing for various scenarios,” Kamiński tweeted. “One of them involves the provincial governors taking action related to a potential influx of refugees from Ukraine who might be looking for shelter in our country, due to the potential conflict.”
According to US intelligence agencies, Russia has encircled Ukraine with around 100 battalion tactical groups, more than half of their total number, the broadcaster NBC reported.
They would be able to reach the capital Kyiv in 48 hours, the Pentagon said.
Amid the escalating tensions in the region, several countries have advised their citizens to avoid all travel to Ukraine, while urging their Ukraine-based nationals to leave the former Soviet republic.
These countries include Italy, the Netherlands, Belgium, Sweden and Spain. Earlier, similar guidance was issued by the United States, Britain, Latvia, Norway, Japan, Canada and Israel.
Meanwhile on Saturday, US President Joe Biden held a phone call with his Russian counterpart Vladimir Putin for the fourth time since the crisis began, the PAP news agency reported.
White House officials said the talks had been “professional and substantive” but failed to generate any “fundamental change” in the dynamic which has been unfolding in the crisis over Ukraine.
Poland’s Prime Minister Mateusz Morawiecki on Sunday warned that the continent was “on the verge of war” and called for “European unity.”
In 2014, Russia annexed the Crimea peninsula from Ukraine and then fomented a separatist conflict in that country's eastern Donbas region, leading to a wave of EU and US sanctions against Moscow and Russian officials.