Shaw will be joined on the 18 July flight to Los Angeles by fellow England World Cup squad member Wayne Rooney.
Spain's Juan Mata and David De Gea are also named, plus Japan's Shinji Kagawa.
"We are delighted to have such a strong travelling squad for our pre-season tour to the United States," said assistant manager Ryan Giggs.
|Manchester United tour dates|
|23 July v Los Angeles Galaxy|
|26 July v AS Roma (Denver)|
|29 July v Inter Milan (Washington)|
|2 August v Real Madrid (Michigan)|
|4 August Champions Cup final (Miami)|
United have already confirmed new manager Louis van Gaal will be present, even though he could be involved in the World Cup final with Netherlands, only five days before his squad leave Manchester.
Van Gaal's side have a minimum of four games in the US, starting against Los Angeles Galaxy on 23 July and including an International Champions Cup programme against Roma, Nemanja Vidic's new club Inter Milan and Real Madrid.