De Lange is the second member of Graeme Smith's touring party to have to return home before the first Investec Test, following wicketkeeper Mark Boucher's career-ending eye injury. He will be replaced by pace-bowling all-rounder Albie Morkel.
Twenty-one-year-old De Lange, who has played just two Tests to date, discovered the extent of his injury after a scan on Friday.
South Africa physiotherapist Brandon Jackson said: "Marchant has been diagnosed with a lower-back stress fracture and will require at least six weeks' rest and rehabilitation.
"A bone scan was done after his lower-back pain worsened in the past week, showing inflammation in the bottom vertebrae of the spine."
Big-hitting Morkel, the 31-year-old older brother of South Africa seamer Morne, therefore has the chance this summer to add to his solitary Test cap.
The tourists are hoping Morkel's experience of English conditions, with Somerset, may be a significant asset.
National convenor of selectors Andrew Hudson said: "Albie is the ideal replacement for Marchant, because he comes into the squad with invaluable knowledge and experience of the UK conditions.
"He has a good first-class record, and his ability to swing the ball and to contribute with the bat lower down the order gave us the extra incentive to rope him in."