The 30-year-old will definitely miss the first game of Poland’s qualification campaign for the 2022 World Cup in Qatar, against Hungary on Thursday.
He must await the results of a second test before finding out whether he will be available for Sunday’s meeting with Andorra and next Wednesday’s fixture against England at Wembley.
Klich has not shown any symptoms or felt unwell.
Jakub Kwiatkowski, media officer of the Polish FA, tweeted: “The Polish national team received the results of the SARS-Cov-2 test this morning.
“Unfortunately, in the case of Mateusz Klich, the result is positive. The competitor is well and shows no symptoms of illness, but his trip to Budapest is excluded. Today the test was repeated.”
Additional reporting by PA.