The Bath winger will remain with England for his rehabilitation, ahead of the tournament that starts next weekend.
"It's disappointing for Anthony and for England but we know he'll rehab diligently to get himself right as soon as he can," Jones said in a statement.
"We're confident he'll be in the mix later for the championship."
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England start against France at Twickenham on Saturday.
(Reporting by Steve Tongue; Editing by Toby Davis)
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