The Leinster back, who started at full-back in Dublin and in the previous week's defeat to the All Blacks in Chicago, was forced off in the second half on Saturday.
The 23-year-old, who had been covering for first-choice full-back Hugo Keenan, will miss the match against Australia on November 15 and the clash with Rugby World Cup holders South Africa the following week.
Centre Garry Ringrose and Leinster teammate Josh van der Flier both have minor hamstring strains and will be assessed during the week.
Mack Hansen has linked up with the squad following a foot injury while centre Stuart McCloskey, who missed the Japan game with a groin problem, is expected to take a full part in training.
The Wallabies are bidding to bounce back from successive defeats. They were shocked 26-19 by Italy on Saturday and lost 25-7 to England the previous week.