Midfielder Mateusz Klich was the first squad member to return a positive COVID-19 test last week and it was revealed on Sunday that goalkeeper Łukasz Skorupski had also contracted the virus.
Polish Football Association spokesman Jakub Kwiatkowski confirmed midfielder Krychowiak and defender Piatkowski have now tested positive on the eve of the clash with Group I leaders England at Wembley.
Kwiatkowski tweeted: "The Polish national team has undergone further tests for the presence of coronavirus.
"Unfortunately, the results of Grzegorz Krychowiak and Kamil Piatkowski are positive. Due to the fact that Krychowiak is a recovering man, we started talks with UEFA in order to clarify the matter and admit him to the match."
Kwiatkowski said he too had tested positive for COVID-19.
Prolific Poland captain Robert Lewandowski has also been ruled out of the encounter with Gareth Southgate's side due to a knee injury.