It's understood that wicketkeeper-batter Josh Inglis and all-rounder Beau Webster are the frontrunners to take Khawaja's place in the XI, with Australia not choosing to call up a replacement member for the squad.
Travis Head's outstanding performance as a fourth innings opener in Perth makes him an obvious choice to fill Khawaja's shoes as the opener in Brisbane, with the strokeplayer telling reporters last week he was open to batting anywhere in the order.
Khawaja's omission comes as somewhat of a surprise after he batted for 30 minutes in Brisbane on Monday, albeit only facing sidearm bowling from batting coach Michael di Venuto, before expressing to the media that he was no longer requiring painkillers and "should be right" to start on Thursday.
Australia's final training session on Wednesday will now be a final opportunity for Webster and Inglis to make their case for Test selection, though team management almost certainly would have been working on plans A and B for Khawaja.
Bowlers Pat Cummins and Josh Hazlewood have already been ruled out of the second Test.
Meanwhile, England announced on Tuesday afternoon that Will Jacks will bat at number eight in England's XI.
Jacks had come into contention on Monday when he and Bashir both bowled at captain Ben Stokes for a lengthy period of time amongst a backdrop of speculation that England were leaning towards a spin option instead of the all-pace attack they took to Perth.
He last played Test cricket on England's December tour of Pakistan in 2022, making 89 runs and taking six wickets in two matches, but has since come a long way on the white ball scene, whilst he has match practice under his belt having played in both England Lions tour matches last month, albeit with no great success.
England 2nd Test XI to play Australia:
Ben Duckett, Zak Crawley, Ollie Pope, Joe Root, Harry Brook, Ben Stokes (captain), Jamie Smith, Will Jacks, Gus Atkinson, Brydon Carse, Jofra Archer
Australia 13-man 2nd Test squad:
Batters: Alex Carey (wk), Travis Head, Josh Inglis (wk), Marnus Labuschagne, Steve Smith (c), Jake Weatherald
All-rounders: Cameron Green, Michael Neser, Beau Webster
Bowlers: Scott Boland, Brendan Doggett, Nathan Lyon, Mitchell Starc