Marsh suffered back stiffness during his innings of 44 on the first day of the opening Test in Cape Town.
He was unable to walk on Wednesday night after batting and wasn't able to field for the entirety of the match.
It's the second time Warner has been called in as a cover player on consecutive tours, after he was flown to Sri Lanka to shadow for Ricky Ponting who returned to Australia for the birth of his second child.
Warner is hoping for a Test debut and will be competing for a spot with NSW teammate Usman Khawaja who is already with the squad in Cape Town.
Warner will depart Sydney on Monday morning (AEDT) to join the Australian squad in Johannesburg ahead of the second Test.
The news is a setback for Marsh after Australia were quietly confident he was improving as he moved more freely around the team hotel.
But it became obvious his fitness wasn't going to improve in time for the start of the second Test at The Wanderers on Thursday.
The left-hander trudged out to bat during Australia's disastrous second innings of 47 at Newlands but his discomfort was obvious and he was trapped lbw for a duck on the second ball he faced.
Marsh has made a fantastic start to his Test career, but the 28-year-old does have a history of back problems.
The decision further enhances Warner's status as a likely Test player in the eyes of selectors.
The 25-year-old has been batting well for NSW and will be in competition for a Test spot with state teammate Khawaja, who is yet to be used so far on the South Africa tour.
Warner himself only flew back home from the rainbow nation just over two weeks ago after taking part in the Twenty20 and ODI legs of the campaign.
"David has been in tremendous form for NSW in all forms of the game, including a recent century for NSW in the Sheffield Shield competition," chairman of selectors Andrew Hilditch said.
"We are certain that should the opportunity present itself, he will be ready to perform at Test level."
Australian team physiotherapist Alex Kountouris said Marsh would undergo further tests at home.
"Shaun injured his back while batting during the first Test in Cape Town," Kountouris said.
"He was in considerable pain and was obviously restricted while batting in the second innings.
"He is slowly improving but will return to Australia for further investigation and treatment as he will not recover in time to play the Second Test in Johannesburg."