A replacement may be presented on Thursday when Boniek will hold a press conference.
Brzeczek received the national team captain's assignment after the WC 2018 and has led the team to the EC.
His contract expired last summer, but was extended until the end of 2021 when the European Championships were postponed.
Poland starts the World Cup qualifier in March.
The European Championship group, with Sweden and Poland, also consists of Spain and Slovakia.