Steyn left the pitch mid-over twice on day three and was taken for scans but they showed no sign of a muscle tear.
The world's top-ranked bowler had a morning fitness test at Kingsmead but again felt discomfort.
The 32-year-old will have more tests to see if he will be fit for the second Test, which starts on 2 January.
The doubts over Steyn's fitness added to the problems for South Africa, who trailed England by 261 runs before the fourth day of the series opener and were facing a struggle to save the game.
The right-arm bowler had only just returned to the Proteas side after missing the majority of their tour of India with a groin injury.
South Africa have also been disrupted by speculation about the future of star batsman AB de Villiers.
The 31-year-old, who is also keeping wicket during this Test, said on Monday that he was looking to ease his workload amid rumours he is considering retiring.
"There are a lot of rumours flying around I hear, but for the last two to three years the only talk I've been doing is to keep myself fresh and to have a bit of rest here and there," said De Villiers, who is ranked the number three Test batsman in the world.
"It's always been the most important thing for me to enjoy my cricket. It's just important to look at the schedule and for me maybe not to play all kinds of cricket.
"That's the only thing that I've been talking about. To keep myself fresh and to keep enjoying the game. I love representing my country and nothing has changed."
South Africa pace bowler Dale Steyn will not bowl again in the first Test against England because of a right shoulder spasm.