England left-back Shaw, signed from Southampton in the close season for around £30 million, may be out for a month with a hamstring problem and will definitely miss the start of the Premier League campaign at home to Swansea City on Saturday.
Verheijen called fellow Dutchman Van Gaal a "great appointment" by United but at the same time accused the former Netherlands manager of "incompetence" and of working his players too hard.
"What LVG proves is that top coaches are not perfect. Even the world's best have deficiencies," Verheijen said on his Twitter feed.
"LVG is tactically superior to most other coaches but planning & periodisation is not his strongest point: double sessions & muscle injuries," added the Dutchman, an expert on football fitness and a frequent critic of the methods of top coaches.
Verheijen questioned why Shaw, 19, cut short his post-World Cup break and said he reported back for pre-season training too early.
Van Gaal accused the left-back of being unfit on their pre-season tour of the United States.
"Luke Shaw had to do extra training to get fit. Who was in charge of his individual programme?," asked Verheijen.
Verheijen suggested Van Gaal's methods were responsible for a spate of injuries among the Dutch players before and during the 2014 World Cup in Brazil, a tournament where they finished third.
"During the World Cup preparation the Dutch players had to do frequent double sessions so not surprisingly the muscle injuries accumulated," he said.
"At Man United, in the first few weeks, LVG has applied the same approach and, as expected, with the same result.
Last season Verheijen attacked the training methods of Van Gaal's United predecessor David Moyes after Dutch striker Robin van Persie was injured.
He has also been critical in the past of top managers like Roy Hodgson, Roberto Mancini and Chris Coleman.
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- Manchester United
- Luke Shaw
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