The injury will see the centre-back miss the forthcoming Premier League games against Norwich and Tottenham.
Jones is also expected to miss the FA Cup tie against Swansea in January and the Capital One Cup semi-final first-leg at Sunderland.
United released a statement just ahead of the clash with Hull City on Thursday.
“We can confirm Phil Jones has suffered a knee injury and is expected to be out for a couple of weeks,” the statement from United read.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
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