The Polish team was among the top seeds for the draw in Dublin on Sunday despite a string of disappointing performances this year.
"We were among the top seeds, and the draw is definitely not the worst possible outcome for us, though our qualifying group is a balanced one,” Poland manager Jerzy Brzęczek said after the draw.
“I think most games will be touch and go, and we have to prepare for that," he added.
Fifty-five teams were drawn into a total of 10 qualifying groups, five groups of five teams and five six-team groups.
Qualifiers will be played between March and November next year, with the top two teams from each group qualifying directly for the championships.
The Euro 2020 tournament will be held from June 12 to July 12, 2020 in 12 cities around Europe, with the final played at London's Wembley Stadium.
The venues are Amsterdam, the Netherlands; Baku, Azerbaijan; Bilbao, Spain; Bucharest, Romania; Budapest, Hungary; Copenhagen, Denmark; Dublin, Ireland; Glasgow, Scotland; Munich, Germany; Rome, Italy; and St. Petersburg, Russia; in addition to London.
Poland made it through to the quarterfinals of the Euro 2016 championships in France, losing to Portugal on penalties.
Brzęczek took over as Poland manager this summer after the national squad’s early exit from the World Cup in Russia.
Poland last month drew 1-1 with Portugal in their last Nations League group match, having already been relegated to a lower tier of the new competitive football format in Europe.
EURO 2020 qualifying groups
Group A: England, Czech Republic, Bulgaria, Montenegro, Kosovo
Group B: Portugal, Ukraine, Serbia, Lithuania, Luxembourg
Group C: Netherlands, Germany, Northern Ireland, Estonia, Belarus
Group D: Switzerland, Denmark, Republic of Ireland, Georgia, Gibraltar
Group E: Croatia, Wales, Slovakia, Hungary, Azerbaijan
Group F: Spain, Sweden, Norway, Romania, Faroe Islands, Malta
Group G: Poland, Austria, Israel, Slovenia, FYR Macedonia, Latvia
Group H: France, Iceland, Turkey, Albania, Moldova, Andorra
Group I: Belgium, Russia, Scotland, Cyprus, Kazakhstan, San Marino
Group J: Italy, Bosnia & Herzegovina, Finland, Greece, Armenia, Liechtenstein
Source: TVP Sport, PAP, uefa.com