"We are all hugely disappointed for Danny who has worked extremely hard and has been an important part of the squad throughout our Rugby World Cup preparations," said Johnson.
"He featured in both warm-up fixtures and was on course for selection so this injury is really disappointing for him personally and for us as a squad. Nobody wants to see a player ruled out at this stage through injury and we all wish Danny a speedy recovery."
ENGLAND POOL B FIXTURES
v Argentina (10 September)
v Georgia (18 September)
v Romania (24 September)
v Scotland (1 October)
Former England centre Jeremy Guscott believes Care could have edged out his rival for a starting place in the team's World Cup opener against Argentina in Dunedin on 10 September.
"In the two warm-up games, I had been very impressed with Danny Care. I think he has been playing the best rugby he has yet for England," he said.
"He has been playing with authority and not trying to take on too much, which he has been guilty of in the past.
"If Care had still been there for that first match, I think it would have been a coin flip between them."
"They definitely have to take three now," England World Cup-winning scrum-half Matt Dawson told BBC 5 live. "It is a big blow for the England side because they are now low in the scrum-half department.
"I think Ben Youngs will be the starter but Joe Simpson could be one of those players who comes from nowhere, gets a little break and he could be a little star. He is a fantastic player, with blistering pace."
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