Papastathopoulos was sent off after receiving two yellow cards in Friday's Group A match, which finished 1-1, while Szczesny got a straight red.
UEFA said that the one-match suspension was in line with the rules, which can be applied unless there are other aggravating disciplinary factors.
No aggravating factors were reported in the dismissals. Papastathopoulos will be available for Greece's final group match against Russia and Szczesny for Poland's game with the Czech Republic, both on June 16.
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