Bracewell suffered the injury playing for Worcestershire Rapids in the English T20 Blast and will undergo surgery in Britain on Thursday.
The 32-year-old spin-bowling all-rounder is expected to need six to eight months to recover.
"Firstly, you always feel for the player when injury strikes and especially when it means they will have to miss a world event," New Zealand head coach Gary Stead said in a statement.
"Michael’s naturally pretty disappointed, but also pragmatic in acknowledging that injuries are a part of sport and he's now turning his focus to his rehabilitation."
New Zealand were runners-up to hosts England at the last 50-over World Cup in 2019.
India are hosting this year's tournament in October and November, with dates to be confirmed.
