The centre-back has suffered a knee injury and will miss the forthcoming Premier League games against Norwich and Tottenham.
United released a statement on social media just ahead of Thursday's match with Hull City at the KC Stadium.
"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.
Jones is also set to miss the FA Cup tie against Swansea at Old Trafford next month and the Capital One Cup semi-final first-leg at Sunderland.
Moyes is already without striker Robin van Persie, who has a thigh problem, while midfielder Marouane Fellaini is absent following wrist surgery.