The Brazilian was rarely used by United last season and was loaned out to Serie A side Fiorentina for the second half of the campaign.
And the 26-year-old, who moved to Old Trafford from Porto in 2007, will not have the chance to impress new United manager Louis van Gaal during their pre-season preparations due to the injury, which he sustained in training.
Instead Anderson will remain at the club's training complex for rehabilitation, with Bebe also not named in the 25-man squad.
Javier Hernandez, Patrice Evra, Marouane Fellaini, Adnan Januzaj, and Robin van Persie will all stay at home after reaching the knock-out stages of the World Cup with their respective national teams.
Michael Carrick is another to miss out following ankle surgery that is expected to keep him sidelined for up to 12 weeks.
United play their first of four games in the USA against Los Angeles Galaxy in the Chevrolet Cup on July 23.
