Vunipola's Saracens club expected him to be out for up to 12 weeks and his absence puts a significant dent in England's No 8 resources for the tests against South Africa, New Zealand, Japan, and Australia in November.
The Vunipola brothers, Mako and Billy, both limped off as did young lock Nick Isiekwe, who made his England debut a year ago.
Both Vunipola brothers - Mako and Billy were forced off with respective injuries in the game at Scotstoun.
Billy Vunipola has struggled for more than a year to play a sustained spell of rugby.
He recently returned to action after fracturing his right arm during England's summer tour of South Africa.
Sam Simmonds was already out after tearing knee ligaments and Nathan Hughes faces a disciplinary hearing on Wednesday.
Gloucester's Ben Morgan, deemed surplus to Test requirements since the 2015 World Cup, is fit and in form, so could now come into head coach Jones' reckoning.
The news around Vunipola will make grim reading for Eddie Jones whose options at No.8 are dwindling ahead of their four-Test November programme.
The injuries are piling up for England, with lock Joe Launchbury last week ruled out after knee surgery.