Mariusz Kaminski took to Twitter on Sunday to assure that the Polish government is ready for such a possibility.
"It is obvious that in connection with the situation in Ukraine we have been preparing for different scenarios," the interior minister wrote.
"One of them includes activities by (Polish) province governors related to the potential influx of refugees from Ukraine, who may be looking for shelter in our country as a result of the potential conflict," Kaminski added.
Kaminski's deputy, Maciej Wasik, said on Friday that Poland "will be prepared for the arrival of a wave of up to a million people."
Ukraine shares its border with EU members Poland, Romania, Slovakia and Hungary, but has had the closest ties with Poland where over a million Ukrainians have emigrated over the recent years in search of a better life.
Russia has massed more than 100,000 troops near its border with Ukraine and has demanded concessions from Nato, including assurances that the bloc will not accept any new eastern members. Moscow and Minsk have also started joint military manoeuvres that are being closely watched by Nato.
On Saturday, US President Joe Biden and Russian President Vladimir Putin talked on the phone for the fourth time since the crisis began, but the conversation did not lead to any breakthrough in the standoff. (PAP)