Canterbury Kings captain McConchie last represented New Zealand in April 2024 and joins the squad off the back of a successful domestic T20 campaign as the Kings’ leading wicket taker with 14 wickets at an economy rate of 7.71.
Black Caps head coach Rob Walter said he was saddened for Bracewell.
“We’re all feeling for Michael,” said Walter.
“It’s really tough to get ruled out of a World Cup and I know how much playing for New Zealand means to him.
“Michael worked incredibly hard to give himself a chance but unfortunately has had this setback.
“We wish him a smooth recovery.”
Walter said McConchie, who has played 145 T20s (12 of them internationals), would bring valuable experience.
“Cole is a seasoned campaigner.
“He brings a great all-round skillset to the group with a lot of T20 experience.
“It’s great to be able to lean on an experienced head, especially for a World Cup.”
McConchie is set to assemble with the squad on Friday.
The Black Caps will play their third Group D match on Sunday, against South Africa, at 2.30am NZT.