The 30-year-old, who needs an operation, was injured in last Sunday's 1-0 win over Liverpool at Anfield.
His absence adds to a list of injuries in wide positions and Van Gaal admitted he is looking to bring in new signings.
"I need full-backs," said Van Gaal. "I have used youngsters a lot of times. Borthwick-Jackson and Varela are doing great but the level at Manchester United is high.
"It is very difficult for youngsters to do that every week. That is why we have to look for reinforcements. We are looking but the clubs don't want to sell. Everybody thinks it is easy but it is not so."