Gareth Southgate names his England Under-21 squad for the tournament on Wednesday.
Shaw has spoken of his desire to represent the Young Lions in the Czech Republic, but Van Gaal would prefer it if he stayed at home.
Shaw has suffered from a number of injuries this season - the latest came in United's win over Crystal Palace last Saturday - and Van Gaal thinks the 19-year-old would benefit from a period of rest instead.
"He needs that rest
He over-crossed his limits
He is 19-years-old
What can you expect? We have to protect him and I hope that the coach (Southgate) understands that," the United manager said.
Shaw has had a difficult first year at Old Trafford.
Van Gaal criticised Shaw for turning up to pre-season out of shape but then hailed the £28million signing as an example after he battled his way back to fitness.
But just after he returned, Shaw was sidelined with a hamstring injury and had to wait until September 27 to make his United debut.
He was ruled out for a month with an ankle injury in November and in March he was sidelined for five weeks because of yet more hamstring trouble.
Speaking last October, Shaw underlined his desire to play in the Under-21 tournament despite already having four full England caps.
The former Southampton left-back said: "I still feel I can go and help out
I'm really looking forward to it.
"Of course I would want to go to the Euros, I always want to help out my country and I know there are few other lads who can also drop down as well that summer."
Shaw is unavailable for Sunday's final home game of the season against Arsenal after receiving an elbow to the face from James McArthur at Palace last week.
Wayne Rooney will also miss the match as he has not recovered from the dead leg he suffered in the win at Selhurst Park .
Jonny Evans is doubtful due to an unspecified injury, but Rafael has recovered from a rib problem that United initially feared would rule him out for the season.
Michael Carrick is out with a calf problem, but Robin van Persie and Angel di Maria are available after sitting out the win in south London due to a virus.
Andreas Pereira is the only other absentee
He is away with the Brazil Under-20 side.
Source : PA
Source: PA