Confirming the news, South Africa team manager Mohammed Moosajee revealed that Quinton had slipped and sustained a freak injury to his right knee at home, Sport24 reported.
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England leads the four-test series 1-0, leaving South Africa under pressure to find a way back in the final two matches.
South Africa put a chaotic morning behind them to post 73 for one at lunch on day one of the third Test against England.
England, who won the first test by 241 runs in Durban, were unchanged, even with several of the side still recovering from a stomach virus that swept through the squad in Cape Town.
Cricket South Africa said Vilas was on his way to Johannesburg but AB de Villiers, who has taken over the South African captaincy, will have to also fill in as wicketkeeper if South Africa fields first at the Wanderers.
It ended a grafting opening partnership of 44 runs with Dean Elgar as the home side negated much of the early advantage that the overcast conditions and a green top offered to the seamers.
Initial signs were good, with clouds overhead and a couple of awkward deliveries from James Anderson and Stuart Broad at the start of their spells.
Finn (2-50) was rewarded for his accurate and disciplined bowling at the Wanderers, while Stokes (2-53) – who scored England’s fastest double Test century in the drawn second Test – also impressed with the ball.
South Africa lost regular wickets after Amla’s dismissal, falling from 117 for 1 to 185 for 5 and then 225 for 7, but had reason for cheer as Chris Morris and Kagiso Rabada batted an hour and saw off nine overs from the second new ball to reach stumps on 26 and 20 respectively.
Moeen Ali was the first to strike, Elgar offering Bairstow more catching practice after edging a delivery that offered enough turn and bounce to deceive the opener.
But England, with a handful of players seemingly suffering from the sickness bug affecting their camp, battled back.
He arrived 30 minutes after play started but with South Africa winning the toss and batting first, his late appearance went unnoticed.
De Villiers had compiled a dashing 36, mostly at Moeen’s expense, but gave it away when Stokes dug one in around his ear.
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Faf du Plessis (16) then popped Finn to Alex Hales at backward square, before Bavuma was run out in calamitous circumstances following a mix-up with Vilas.
