Starc and Green will miss the New Year's Test after both players suffered finger injuries in the innings and 182-run smashing of the Proteas at the MCG.
Despite suffering a finger tendon injury on his bowling hand on Boxing Day, Starc bravely continued to bowl and bat for the remainder of the Test to help Australia seal the series.
The left-armer will aim to get himself right for February's blockbuster tour of India.
"I think (I will be) getting another scan in Sydney and seeing a finger specialist to work through all that," Starc said.
"Obviously India's coming up so we'll see what timeframes are in after I've had those discussions and hopefully it fits in somewhere at the front end of the tour.
"Apart from the finger being out of action, I can still train to some degree and just finding creative ways to keep the workloads up."
Fellow NSW quick Josh Hazlewood has declared himself fit after he missed a third-straight match when he pulled himself out of contention at the MCG with a side-strain injury.
Selectors would have been forced to choose between Hazlewood and popular Victorian Scott Boland if the 58-Test paceman had been fit to play.
It was a rollercoaster week for Green after he was bought for $3.15 million in the IPL auction, claimed his maiden five-wicket Test haul, but was struck on the hand while batting on Tuesday.
Green retired hurt on nine, but returned to bat on Wednesday and finished unbeaten with a gritty 51.
However, the 23-year-old did not take to the field during South Africa's second innings and will rest ahead of the India tour.
"Greeny is pretty close to being irreplaceable as a top-order batter that gives you another bowling option," captain Pat Cummins said.
"We'll chat through all those combinations when we get a bit closer (to the SCG Test) but we're not not settled on anything."
Cummins said selectors would factor in India when picking an XI to play at the SCG.
"It's probably going to be the wicket in Australia that most closely resembles India, even if it doesn't spend big," he said.
"It might give us a chance to have a look at one or two players that will be on that Indian tour but the first priority is of course to win the Test match."
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