Teenager Shaw, who represented England at the recent FIFA World Cup in Brazil, completed a high-profile move to United from Southampton last month.
However, it would appear he has work to do if he is to earn a place in Van Gaal's line-up for the Premier League opener against Swansea City at Old Trafford on August 16.
Shaw trained separately from his team-mates at Washington's FedEx Field, ahead of United's International Champions Cup fixture against Inter, before sitting out parts of Monday's session.
Asked to explain why, Van Gaal said: "He is OK, but I am always a trainer-coach who sees individuals and what they need. He needs to be fit and is not very fit or fit enough to do what I want. He needs to train individually until he is fit."
United's Dutch manager went on to concede he is unsure how long it will take for Shaw to reach a level of fitness he finds acceptable.
"I cannot judge how long that will take, but I see what I see," added Van Gaal.
"I have spoken with him and we have made a programme for him. He agreed with me.
"How long [until he is fully fit]? That we have to see, but that I don't know.
"I have heard good messages from Strud [United fitness coach Tony Strudwick], but we have to see."
Van Gaal also explained the reasoning behind Rafael, who has a groin problem, returning to Manchester for treatment.
"You can leave the player in America and treat him here, or choose to have the best treatment and we think it is much better at the Aon Complex [United's training ground]," said Van Gaal.
"He can work out his jetlag much quicker if he goes home. There are two arguments for it and he agreed with me that he should go back.
"He is already back, but we will wait and see how long he takes."
