The England international made his United comeback after four games out with a hamstring injury in the 2-2 draw at West Bromwich Albion on Monday, but didn't feature in the Old Trafford game against Jose Mourinho's charges, which finished 1-1.
Van Gaal told reporters after the game: "The match against West Brom was his first after a long injury period. We brought him back and he trained for more than a week with the first team, then had to play 90 minutes.
"Then he had a sore feeling in his shin. On Saturday he could not continue training, even though it was a very light session before the match. He had shin splints, which is very painful.
"I don't know how long it will take [for him to recover]."
Manchester United are currently eighth in the Premier League table.