The Poland international had to come off during their eventual Euro 2024 play-off semi-final win against Estonia.
Cash will now miss the run-in for Villa, as he is set for at least three weeks on the treatment table with a hamstring issue.
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Per the Birmingham Mail, the club will have to do without the full-back for games against Wolves, Manchester City, Brentford, and a Europa League two-legged tie against LOSC.
However, Cash will be hoping that he can be back for the latter games, as Villa chase fourth place in the Premier League.