The 23-year-old made an impressive debut off the bench in the Springboks' series-opening 22-17 win in Durban on Saturday but now faces up to three months out with a bulging disc.
Dean Greyling had already been called into the squad as cover and will now officially take Oosthuizen's place.
Springboks coach Heyneke Meyer said: "Coenie has brought a lot of energy to our team and he played a major part in our victory in the first Test, making a big impact when he came on.
"The player's welfare comes first and we decided that it would be best for Coenie to get some proper rest and rehabilitation now.
"Hopefully he'll be back to full fitness soon. He definitely has a role to play in future."
Team doctor Craig Roberts said: "We will follow a conservative approach with Coenie. He is still a young player and has a long career ahead of him and needs to be managed appropriately."
The news is South Africa's second injury blow after full-back Zane Kirchner was ruled out of the second Test with a knee problem.
Gio Aplon has been added to the squad but Kirchner's place in the side is likely to go to Pat Lambie, who came on as a substitute in Durban.
Greyling could come into contention for the second Test, for which the side is due to be announced by Meyer on Thursday.
Meyer said: "Dean brings experience to the squad and, like Coenie, he is a loosehead that can play tighthead if needed.
"He now has an opportunity to show what he can do and he needs to grab it."
England have also had injury problems with full-back Mike Brown out for the series with thumb ligament damage and centre Brad Barritt out of the second Test after surgery on a lacerated eyeball.
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