Johnson said on Friday: "As I said on Wednesday, Jonny was being assessed day-by-day and we would have a better idea of where he was in terms of the injury by the end of this week.
"It's clear that Jonny will need a period of rehab of around four weeks and this will be carried out in conjunction with Toulon."
Wilkinson, who has won 80 caps, has been in sparkling form for his club side and was in a battle with Toby Flood to win the England number 10 shirt.
England will pressurise NZ - Johnson
The 2003 World Cup winner has featured for England in every Test in the past 12 months, but has been plagued by injuries since slotting the drop-goal to beat Australia in the final seven years ago.
England have been given an injury boost with the news captain Lewis Moody will be fit to play, despite damaging the retina in his left eye on 1 October.
He has been released to play for Bath in their game against Harlequins on Sunday before returning to the England camp.
But there are still concerns over Wasps' pair Riki Flutey and Simon Shaw, who have not trained this week after suffering calf injuries, while Hendre Fourie has returned to training after taking a bang to the ribs in Leeds's defeat by Sale on Friday night.
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