The injury was confirmed following scans conducted on Monday, and Nortje is not expected to recover in time for the 50-over tournament.
The Proteas are set to kick off their campaign against Afghanistan on February 21 in Karachi, Pakistan.
A replacement for Nortje will be announced by South Africa in the coming days.
This marks the second consecutive ICC event Nortje will miss, as he was also unavailable for the 2023 Cricket World Cup in India due to a stress fracture in his back.
