The ministry said the controls should not obstruct fluent travel and would be conducted on selected days from June 4 to July 1 at chosen border crossings with Germany, the Czech Republic, Slovakia and Lithuania.
Border control staff would have access to databases and equipment to verify documents and test for drugs.
Poland, an European Union member since 2004, is part of the EU's border-free Schengen zone.
"In case a person is identified who may pose a threat to security or public order, a decision will be issued to deny this person's entrance to the territory of Poland," the statement said.
Poland, co-host of the June 8-July 1 tournament with Ukraine, is expected to attract more than 800,000 visitors to the cities of Warsaw, Gdansk, Wroclaw and Poznan where matches will be held, according to a government-funded report.