United have announced that left-back Shaw has suffered a hamstring injury.
Shaw, who joined the Red Devils from Southampton in June for £27million, is expected to miss United's first three Barclays Premier League games, including their opener against Swansea on Saturday.
A statement on United's website read: "Luke Shaw has suffered a hamstring injury and will miss the opening game of the season against Swansea City on Saturday.
"The England international, a summer signing from Southampton, is likely to be sidelined for around four weeks.
"Shaw sat out the friendly victory against Valencia at Old Trafford due to the problem and faces a wait before making his competitive debut for the club."
Shaw, who was a member of England's World Cup squad in Brazil, has been struggling with his fitness since joining up with his new team during their pre-season trip to the United States.
The teenager will also miss the games against Sunderland, Burnley and QPR and may not be avalailable until the middle of September.