The 22-year-old was dropped for his country's 28-9 win over Samoa at the weekend and sustained the injury playing for club side Saracens as they lost to Northampton Saints in the Aviva Premiership.
Exeter Chiefs number eight Thomas Waldrom replaces Vunipola in England coach Stuart Lancaster's 34-man squad for the visit of the Wallabies.
Flyhalf Stephen Myler, who kicked 16 points for Saints in their victory over Saracens on Sunday (local time), returns to England's squad having recovered from a hamstring problem.