Australian officials confirmed on Wednesday that Smith had undergone scans on Friday, before failing in his bid to play in the third and deciding Test.
Those scans detected an injury to a "cervical facet joint" which connects to the spine and acts to guide and stabilise neck movement.
"Due to this and his limited range of motion, he was unfit to participate in the current Test," Cricket Australia said in a statement.
"Steve will continue to receive treatment and rehabilitation, with a full return to availability anticipated for the upcoming home Test series against New Zealand."
Smith has six weeks to recover for the first Test against New Zealand, which will begin a long run of virtually uninterrupted cricket through to mid-March.
Australia will want Smith available for that stretch of 10 Tests in 14 weeks, just as they had hoped to have him for the return to Cape Town this week.
Even well after Friday's scans on arrival in Cape Town, Australia's coaching staff had been extremely confident Smith would be fit to face South Africa.
The 37-year-old batted in the nets for around 35 minutes on Sunday, two days out from the third Test, before sitting down and stretching his neck.
He then briefly returned to batting, before growing increasingly frustrated and walking out of the nets.
Smith also attempted to bat on Tuesday morning just 90 minutes before the match, then determining he was not able to get his neck right.
"He is huge, one of the greatest batters we have ever had," Cummins said on Monday.
"You don't play 100-odd Test matches without playing Test matches where you're not 100 per cent fit.
"Even though he is probably not going to be 100 per cent hopefully he can compartmentalise that, like he has done a hundred times before with other things, and come out and contribute like he does every week."
The injury means Smith is likely to never play another Test at Newlands, the venue of the ball-tampering scandal in 2018 that cost him the captaincy and a 12-month ban.
19°C