The squad features 10 players who took part at the World Cup, including Wayne Rooney, as well as the club's summer recruits, Luke Shaw and Ander Herrera.
Shaw, David de Gea, Shinji Kagawa, Chris Smalling, Phil Jones, Juan Mata, Antonio Valencia, Danny Welbeck and Nani were all eliminated at the group stage in Brazil with their respective countries.
Of United's international contingent, only Patrice Evra, Javier Hernandez, Robin van Persie, Adnan Januzaj and Marouane Fellaini are not included, all of whom reached the second round or further.
The Red Devils will face LA Galaxy in their first match of the summer on July 23 before clashes with Roma, Inter and Real Madrid in the International Champions Cup on July 26, July 29 and August 2, respectively.
Van Gaal has also included some younger players, with the likes of Tyler Blackett and Jesse Lingard given chances to impress.
Midfielder Anderson, who spent the second half of 2013-14 on loan at Fiorentina, does not travel, with the club confirming that he suffered a calf injury in pre-season training.
Squad in full: David de Gea, Anders Lindegaard, Sam Johnstone, Ben Amos, Rafael, Jonny Evans, Chris Smalling, Phil Jones, Luke Shaw, Tyler Blackett, Michael Keane, Reece James, Ander Herrera, Tom Cleverley, Darren Fletcher, Ashley Young, Wilfried Zaha, Shinji Kagawa, Juan Mata, Antonio Valencia, Nani, Jesse Lingard, Danny Welbeck, Will Keane, Wayne Rooney