The right-hander scored centuries in each of the first two games and top-scored for Australia again in Sunday's loss in Sydney.
Finch, who posted 107 at the Melbourne Cricket Ground in the series opener, and added 106 in the second game before hammering 62 in the third game, will be assessed in the coming days before a decision on his availability for Sunday's fifth ODI in Perth is made.
Finch's absence will likely lead to the return of Travis Head, who was dropped for the third game at the Sydney Cricket Ground.
Head and David Warner shared a record-breaking opening stand in the Australia Day clash last year and could resume that partnership exactly 12 months later on Friday.
The form of Finch has been a rare bright spot for the Australians in what has been a horror series so far, with England holding an unbeatable 3-0 lead in the five-match rubber.
England, on the other hand will hope to continue their winning run and bank on their top order's batting prowess to come good in the fourth match.
Squads:
Australia: Steve Smith (Captain), David Warner (vc), Pat Cummins, Aaron Finch, Josh Hazlewood, Travis Head, Mitchell Marsh, Tim Paine, Jhye Richardson, Mitchell Starc, Marcus Stoinis, Andrew Tye, Cameron White, Adam Zampa.
England: Eoin Morgan (Captain), Moeen Ali, Jonny Bairstow, Jake Ball, Sam Billings, Jos Buttler, Tom Curran, Alex Hales, Dawid Malan, Liam Plunkett, Adil Rashid, Joe Root, Jason Roy, David Willey, Chris Woakes, Mark Wood.
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