Shaw has endured a difficult start to life at Old Trafford since his £28million move from Southampton.
Van Gaal made the 19-year-old train on his own during the tour of the United States because he felt the player had turned up to pre-season out of shape.
The United manager was, however, impressed with the way Shaw battled his way back to full fitness, and had it not been for a hamstring injury he picked up just before the start of the season, it seems certain the England left-back would have played in the club's opening two league games.
"I have read nasty articles about Shaw," the United boss said.
"In the United States I said to him 'you came and you were not fit'.
"I changed his programme and he did everything that he has to do to be fit.
"Now he is an example in the dressing room. He is training fantastically."
Given that Shaw has been out for a fortnight with the hamstring injury, it came as something of a surprise to Van Gaal that Hodgson accepted an invitation to speak about the defender's fitness during a press conference at Wembley on Thursday.
Hodgson appeared to suggest he thought Shaw was not currently fit enough.
"If Louis thinks that he can get him fitter then I'm sure he will certainly have our approval," said the England boss, who also claimed he told the player his fitness was not up to scratch at the World Cup.
Van Gaal seemed perplexed by Hodgson's comments.
The Dutchman said: "He is not fit now because he is injured. Roy Hodgson cannot judge at this moment. He cannot judge him because I have never seen him here at a (United) training session.
"I think he is referring to the World Cup. It is possible, I don't know. That is what I want to ask.
"But now Shaw is doing a great job."
Shaw, one of nine United players sidelined through injury, is expected to be fit after England's double-header against Norway and Switzerland.
Michael Carrick could also be back soon as he is making good progress from the serious ankle injury he suffered in the summer, Van Gaal revealed.
"Carrick is also doing a great job," the United boss continued.
"Carrick removed his (protective) boot (on Friday)."
Sam Johnstone, Rafael, Shaw, Chris Smalling, Jesse Lingard, Ander Herrera, Shinji Kagawa, Marouane Fellaini and Carrick are currently out injured for United, who have one point from their first two league games.
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