The 19-year-old, who arrived at Old Trafford in a big-money move from Southampton in June, was not involved as United defeated Valencia 2-1 in their final pre-season friendly on Tuesday.
And the club confirmed on Wednesday that Shaw could be sidelined for around four weeks.
England international Shaw recently faced criticism from new United manager Louis van Gaal over his fitness levels, with the Dutchman saying at the time: "He is OK, but I am always a trainer-coach who sees individuals and what they need.
"He needs to be fit and is not very fit or fit enough to do what I want. He needs to train individually until he is fit."
It now looks as though Shaw will have to wait to impress Van Gaal in a competitive fixture as he races to recover from this injury setback.
United get their Premier League season under way against Swansea City on Saturday.
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