[2] An academy graduate of the former club himself, Drągowski made his Ekstraklasa debut at the age of 16 in a 4–4 draw with Korona Kielce on 27 May 2014.

[3] Following his performance during the match, he was named the division's Best Goalkeeper, Discovery of the Season and voted third-best player overall.

[12][13] In June 2017, Drągowski was one of 23 players named in the U21 squad by Marcin Dorna for the 2017 UEFA European Under-21 Championship, where Poland were the hosts.

[14] In October 2020, Drągowski received his call-up to the Polish senior squad for 2020–21 UEFA Nations League along with three friendly matches against Finland, Netherlands, and Bosnia and Herzegovina.

[15] Drągowski was named in the final Polish 26-man squad for the 2022 FIFA World Cup, but missed the tournament due to an injury and was replaced by Kamil Grabara.