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.
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.

The presenter succeeded Jonathan Ross as host of the revamped weekly show and said leaving "wasn't an easy decision".
Winkleman, who also co-hosts Saturday night show Strictly Come Dancing, said the show "simply deserves someone who can give it their all".
A new series will return this autumn with the new presenter to be announced "in due course", the BBC said.
Winkleman, who lists The Godfather and The Shawshank Redemption as her favourite films, said: "I'm incredibly sad about leaving the film show and it wasn't an easy decision.
"At this time of year I juggle all kinds of things for TV and radio and the show simply deserves someone who can give it their all."
She added that she would miss film critic Danny Leigh, who presents the show alongside her, and the team behind the show.
Mark Bell, BBC head of arts commissioning, said: "We've loved having Claudia on Film 2016 and I'd like to thank her for all her hard work and commitment to the show."
The long-running film show, first broadcast 45 years ago, was fronted by film critic Barry Norman for 26 years. He was succeeded by Ross in 1999, who stayed at the helm for 11 years.
Winkleman will still present the BBC's The Great British Sewing Bee and host a Radio 2 show.
After landing the job on Strictly in 2014 when Sir Bruce Forsyth left, the mother-of-three said of her TV and radio commitments, she would "make it work".
The 14th series of Strictly gets under way on Saturday evening, with Olympians, actors and singers competing for the glitterball trophy.

Many more are feared trapped under rubble after hundreds of buildings collapsed.
Thousands of people have been forced to take refuge in temporary shelters and mosques.
Some have been left homeless after their houses were destroyed, others have fled their homes amid fears of aftershocks and a possible tsunami.
Rescue workers used diggers to remove rubble in their search efforts overnight on Wednesday.
Others used their bare hands and shovels to find people.
A few survivors were pulled out alive on Wednesday.
More than 200 buildings were either seriously damaged or toppled in the earthquake.
The Pidie Jaya region, on the north Aceh coast, was the hardest hit.
The tremor hit just offshore early on Wednesday morning.
Many of the homes in the area have corrugated tin roofs which collapsed.
Hundreds have also been rushed to the sole functioning hospital, which has been overwhelmed by patients.
Banda Aceh, the provincial capital, was one of the worst hit areas by the 2004 tsunami, caused by a massive earthquake.

Remortgaging loans approved in July hit the highest level for nearly seven years, the Bank of England data show.
Mortgage approvals for house purchases also rose to a 17-month high.
Both remain far below the peak of housing market activity, but signal an assumption of imminent rate rises despite market turmoil in recent days.
The economic situation in China created a shock across world markets and some analysts suggested this could delay a rise in the Bank rate in the UK.
The governor of the Bank of England was more circumspect in a recent speech and has hinted that a rate rise could be seen next year.
Homeowners have been increasingly signing up to mortgage deals, especially by remortgaging, in anticipation of a rate rise. This has been encouraged by competition between lenders battling over borrowers' custom.
Howard Archer, chief UK economist for IHS Global Insight, said the Bank's latest figures were "compelling evidence" that housing market activity was firming up.
"It is possible that July's performance may have been lifted by some house buyers looking to move quickly to try and lock in a low mortgage interest rate before they start rising," he added.
Manchester United's £56m new signings Ander Herrera and Luke Shaw will join the squad to tour the United States later this month.
[NEXT_CONCEPT]
Claudia Winkleman has quit the BBC's movie review show, Film 2016, after six years of fronting the programme.
[NEXT_CONCEPT]
A 6.5-magnitude earthquake struck Aceh province in Indonesia on Wednesday, killing at least 97 people.
[NEXT_CONCEPT]
Continued expectations of an interest rate rise are prompting more homeowners to lock into a new mortgage deal, figures suggest.