The pontiff is attending World Youth Day events, a worldwide event which is celebrated every three years in a different country.
Interior Minister Mariusz Blaszczak said that the checks will continue until the start of August.
He said travellers from within the visa-free Schengen zone should carry their passports or other ID documents and others should carry their Polish visas at all times.
Checks will take place in airports, sea ports and on borders with other European Union states, including Germany, the Czech Republic and Slovakia.
The agreement that lets residents of Ukraine and Russia's Kaliningrad area to travel 31 miles into Poland has also been suspended.
Poland often introduces border controls during big events, but security has been heightened further following terror attacks in Europe, most notably in Paris in 2015 and Brussels in 2016.
World Youth Day was celebrated in Rio de Janeiro in Brazil in 2013.
