The 22-year-old suffered the blow during England's 2-0 victory over Switzerland in their opening Euro 2016 qualifier on Monday night.
Van Gaal told reporters in this afternoon's press conference: "Phil Jones may be out for three weeks or a month. But with Jones that is very difficult to say because it it not good to say that, because if it is longer you will say 'Louis, you said three weeks?' That is not good for the player, not good for me, only good for [the media]."
United will face Queens Park Rangers at Old Trafford on Sunday as they hunt for their first competitive win under Van Gaal.