The injury forced him off at half-time during Wasps' European Cup encounter against Toulouse, and he is to remain with his club for further treatment.
Shaw's Wasps team-mate Joe Worsley and Gloucester lock Alex Brown are already sidelined because of injury troubles.
Worsley, Brown and Shaw were all tipped to start against Australia.
England head coach Andy Robinson is due to announce his 22-man match-day squad at Loughborough University on Thursday.
"The England medical team have been in regular contact with London Wasps regarding the back injury sustained by Simon Shaw last weekend, and have decided that Simon should stay with his club for further treatment," said Robinson.
"We will continue to monitor his progress, but it looks likely that he will not be considered for selection for the Investec Challenge match against Australia on November 12.
"At this stage, I do not intend to call up any replacements for Simon, and there are no other concerns regarding injuries."
Bath pair Danny Grewcock and Steve Borthwick are the probable second-row pairing against Australia, with either Pat Sanderson or Andy Hazell entering a back-row equation that could see Leicester's Lewis Moody switched to blindside flanker duties.
Robinson plans to announce his line-up at the squad's Surrey training base on Sunday afternoon.