Vunipola sustained the injury in Saracens' Champions Cup win over Glasgow on Sunday and will be out for around six weeks, Saracens rugby director Mark McCall said on Wednesday.
England were already without Vunipola's brother Billy, who broke his left arm in the same game, for their November tests against South Africa, New Zealand, Japan and Australia.
England's injury list also includes flanker Chris Robshaw, lock Joe Launchbury, fullback Anthony Watson and back-row forward Sam Simmonds.
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England coach Jones names his squad for the November games on Thursday.
(Reporting by Toby Davis, editing by Ed Osmond)
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