The 35-year-old defender will remain at Carrington for treatment on a calf problem when the squad leave on Monday for Chicago, in the hope he will be fit for the start of the new season.
Neville recovered strongly last season after injuries had curtailed his involvement in previous campaigns and was handed a one-year extension to his contract.
United say he suffered a minor setback in training with a small tear to his calf muscle.
Boss Alex Ferguson believes it will be more beneficial for Neville to remain at home than make the trip.
TOUR SQUAD: Edwin van der Sar, Tomasz Kuszczak, Paul Scholes, Ryan Giggs, Dimitar Berbatov, John O'Shea, Wes Brown, Rafael Da Silva, Jonny Evans, Darren Fletcher, Darron Gibson, Chris Smalling, Nani, Fabio Da Silva, Federico Macheda, Daniel Welbeck, Mame Biram Diouf Tom Cleverley, Ritchie De Laet, Corry Evans, Ben Amos, Gabriel Obertan.
Mexico striker Javier Hernandez will join up in Houston on July 27 after arriving from Chivas Guadalajara