The Wales defender suffered a strain during victory over Everton last weekend.
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"It’s bad news. He will definitely be out injured until at least the international break," said Farke.
"He’s a tough boy and it’s a blow for us. Hopefully he’s back on the other side of the break. It’s not ideal. We don’t need to sugarcoat it — Ethan is a big miss."
Given Farke's suggested timescale, Ampadu is set to miss the next three games for Leeds.