The Italy defender was forced off in the 36th minute at the Stadium of Light and left the ground with his arm in a sling to further add to United’s injury problems.
Van Gaal admitted after the game that the setback was “unbelievable” following the Red Devils’ current injury woes, with Marcos Rojo also unavailable after dislocating his shoulder earlier in the season.
Speaking at his post-match news conference, Van Gaal said: “It is unbelievable.
“It is a dislocation so he will be out for several weeks. We do not have many more full-backs, not even in the [youth] system.
“Donald Love has played today at right-back and he did it well.”
Saturday’s defeat left United languishing in fifth place in the Premier League table and with an uphill struggle to secure qualification for next season’s Champions League.
Their next Premier League game is a home clash against Arsenal at Old Trafford on Sunday 28 February.
United finished fourth in Van Gaal’s first season at the club.
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