He has not broken it, but will not be fit for the final autumn international. Gloucester No.10 Freddie Burns comes into the squad.
Owen Farrell, who replaced Flood against the Springboks, is favourite to start in the playmaking role but uncapped Burns is also an option.
The leading points-scorer in the Aviva Premiership, Burns kicked 19 points in Gloucester's 29-3 victory over Sale on Saturday.
The 22-year-old trained with England in the build-up to their games against Fiji and Australia.
"It's a big blow to lose to Toby," England head coach Stuart Lancaster told Sky Sports News.
"Equally there is an excitement in bringing Freddie Burns in. He is one of the form players in the Premiership, if not the form player, and he has trained with us the last couple of weeks.
"He has knowledge of what we do now and what we need to do, we just have to bring him up to speed."
Gloucester prop Nick Wood and Bath wing Tom Biggs have also been brought into the squad after Alex Corbisiero (knee) and Ugo Monye (calf) were ruled out.
"Nick Wood will provide cover as we manage Alex's knee at the start of the week," said Lancaster.
"Tom [Biggs] is next in line from the Saxons and we are looking forward to getting a look at him."
England beat Fiji in their first autumn Test but have since lost to both Australia and the Boks, with the latter an attritional 16-15 defeat in freezing rain at the weekend.
The All Blacks pose the sternest test, having won the World Cup on home soil last year.
Lancaster met with Chris Robshaw on Sunday night and gave his full support to England's under-fire captain. Robshaw's decision-making is under the microscope again after he instructed Farrell to kick for goal when England were trailing 16-12 with just two minutes left.
"Chris and I sat down with the coaches and the whole team and we talked through that and all the other decisions," Lancaster said.
"Chris was our top tackler, our top ball carrier, more breakdowns than anyone; he had an outstanding game. We all felt we had let him down because he had made a decision and it is up to us to make it work. It didn't.
"In hindsight there was a greater probability if we had gone in the corner, but the most important thing for me is we all stood behind the captain and we are all together as a team. We can't hang Chris Robshaw out to dry."
- Sports & Recreation
- Freddie Burns
- Stuart Lancaster