Young, a winger who has filled in at right and left back this season after a string of injuries, was forced off late in the first half of the Premier League victory at Liverpool on Sunday.
Van Gaal told MUTV Young needed surgery and that United could sign a full back in the January transfer window after being forced to use academy players in the position.
"I have started with Valencia, Shaw, Rojo, Darmian and Young, sometimes, and they are all injured -- only Darmian is now back," Van Gaal said.
"So, I need full backs and you have seen how I have used youngsters like Borthwick-Jackson and Varela who are doing great but the level of Manchester United is high."
United's woes at full back started when Luke Shaw suffered a double leg break in a Champions League game against PSV Eindhoven in September.
Utility wide man Antonio Valencia underwent foot surgery in October and has yet to return while Marcos Rojo suffered a shoulder injury and was operated on last month.
Van Gaal has been forced to blood teenager Cameron Borthwick-Jackson and Guillermo Varela in a makeshift defence and the Dutchman said United needed to make additions to the squad.
"To give a high performance every week normally is very difficult for youngsters, which is why we have to look always in this transfer period for replacements," he said.
"The difficulty is that we ask for a level and the clubs do not want to sell in this period and that is our problem. We are looking, but it is not so easy."
(Reporting by Justin Palmer; Editing by Ed Osmond)
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