"It is clear that he cannot play on Sunday but we will try to get him fit for the rest of the tournament hoping Italy go further," team doctor Enrico Castellacci said in a statement after bringing forward medical tests originally due on Wednesday.
Chiellini suffered the injury in Monday's 2-0 Group C win over Ireland and was replaced by fellow centre back Leonardo Bonucci, who is now likely to keep his place alongside Andrea Barzagli against the English.
Toughnut Chiellini has been Italy's most consistent defender in the past four years but made a mistake for Mario Mandzukic's equaliser in the 1-1 draw with Croatia in the group stage.
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