Roy sustained the injury during England’s defeat against South Africa on Saturday in their final Super 12 game.
England, who will take on New Zealand in the first semi-final on Wednesday, have called up James Vince as Roy’s replacement for the remainder of the tournament.
“I’m gutted to be ruled out of the World Cup. It is a bitter pill to swallow,” Roy said in his official statement.
“I will be staying on to support the boys, and hopefully, we can go all the way and lift that trophy. It has been an unbelievable journey so far, and we have to continue expressing ourselves and concentrating on us.
“The rehab has already started, and even though I’ve torn my calf, I’m going to give myself the best chance of being ready for the T20 tour of the Caribbean at the start of next year.”
England are bidding to become the first team to hold the T20I and ODI World Cups at the same time and won their first four Super 12 matches before South Africa snapped that streak.
Roy scored 123 runs across England’s five group stage games, with the highest score of 61 in an eight-wicket victory over Bangladesh.
Sam Billings, who is in the 15-man squad but hasn’t played a game in the ongoing World Cup, could come into the final eleven, with the option of promoting Jonny Bairstow or Dawid Malan as an opener.
Billings has played 32 T20Is for England, amassing 417 runs at an average of 16.68 with the best score of 87.
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