The midfielder missed Thursday's 3-3 World Cup qualifier against Hungary because he was isolating after testing positive upon reporting for international duty.
A negative test then raised hopes that he might be able to return, but a second positive has put him out of the matches against Andorra and England a spokesman for the Polish national team has confirmed.
Normally an ever-present in the Leeds team under Marcelo Bielsa, Klich has been a substitute in four of the last 11 matches as he has struggled with a hip problem, and fatigue. He was substituted in five of the seven starts, three times at half-time.
“Over the last three years I have not had any holidays,” he pointed out.
"Fortunately, I was avoiding more serious injuries, but minor ones started to happen to me from overload, from intensity. My joints don't hurt yet, I'm only 30 years-old, but something hurt.
"At the club, we also train very hard between games, so it's hard to regain freshness. I hope to catch my breath, because I have the best matches when I am physically prepared."
Klich now has until the Easter weekend to get himself ready for his next game. Leeds's first game after the international break is at home to Sheffield United on April 3.
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