The extent of the injury was revealed after the pacer underwent scans on Monday.
Nortje is not in line to recover ahead of the 50-over tournament, which the Proteas will begin on 21 February against Afghanistan in Karachi, Pakistan.
South Africa will announce his replacement in due course.
Watch every wicket of Anrich Nortje from the ICC Men's T20 World Cup 2024.
Every ICC Men's Champions Trophy 2025 squad
Nortje also missed South Africa's previous participation in an ICC event – the Cricket World Cup in 2023 in India – due to a stress fracture in his back.
The 31-year-old's steady variation, bounce and pace have been pivotal in South Africa's pace unit in the white-ball format, proven by his 36 wickets in 22 ODIs and 53 wickets in 42 T20Is.
The right-arm speedster's last outing in the ODI format came over 15 months ago, in the Proteas' second ODI against Australia in Bloemfontein.
South Africa has retained their core group of players that made it to the semi-finals of the ICC Cricket World Cup in 2023, with 10 of their 15 participating members named for the Champions Trophy as well.
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