All Blacks loose forward Adam Thomson, who has an injured elbow, is also set to be ruled out of the hosts' tournament-opening clash with Tonga on September 9, team doctor Deb Robinson said.
Both Thomson and number eight Read sustained their injuries in the defeat against Australia in Brisbane on Saturday.
Team doctor Robinson said in a statement released by New Zealand Rugby: "Kieran has torn the ligament between the tibia and fibula at the front of his left ankle and while it's still early days in his recovery, with aggressive rehabilitation we are aiming to have him available to play near the end of the round-robin.
"Adam's MRI scan shows some swelling around the inside of his elbow which should settle quickly.
"He also has some deep bruising to his upper arm and while it's difficult to know how long that will take to settle, we are hoping he will be ready for selection for the second round-robin match against Japan."
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