Inglis was on Saturday ruled out of the remaining two ODIs against the Proteas, after being sent home for further scans and treatment on his right index finger.
Inglis was hurt while wicketkeeping in Australia's series-opening loss in Durban on Thursday. He remained behind the stumps after the blow and still batted at No.4.
Inglis had stood a legitimate chance to return to Australia's Test team with uncertainty around the batting order and Marnus Labuschagne under pressure.
But he is now in a race against the clock to be fit for the first Test in Durban on October 9, and also has the disadvantage of not being able to press his claims in the preceding warm-up game.
The West Australian has averaged 26.28 across five Tests, with his most recent appearance being in Adelaide during last summer's Ashes.
He made scores of 32 and 10, before immediately dropping back out of the side when Usman Khawaja was fit for Boxing Day.
Beyond Inglis, Australia have Cooper Connolly as the other batting reserve in the squad. Nathan McSweeney looms as the most likely next in line from outside of the group.
It is the second time Inglis has suffered a poorly-timed injury, after a snapped golf club ruled him out of the 2022 T20 World Cup.
Alex Carey is in Australia's white-ball squad for South Africa, and will almost certainly enter the side and take gloves for the second ODI in Johannesburg on Sunday.
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