The 19-year-old has picked up a hamstring injury and the club confirmed he faces a month on the sidelines.
The injury to the left-back is likely to speed up the club's move for Sporting Lisbon's Marcos Rojo who is believed to be trying to force through a transfer to Old Trafford.
United are short of left sided defenders after selling both Patrice Evra and Alexander Büttner in the summer.
Shaw became the fourth most expensive defender in history when he swapped Southampton for United in a deal that could cost the Old Trafford club £30million.
Although he played for England at the World Cup, it is worth remembering Shaw only made his full Premier League debut in November 2012.
Manchester United kick-off the new Premier League season against Swansea City at Old Trafford in Saturday's early kick-off.
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- Manchester United
- Patrice Evra