'Major setback' for the touring side as Atkinson goes off suffering a hamstring problem.
The English seamer increased England's injury problems after leaving the ground during Saturday's play of the fourth Ashes Test versus the Australians.
Atkinson felt a problem in his left leg after the final ball that he bowled on Saturday.
Team management reported the 27-year-old felt some "soreness" and required time off the field to undergo evaluation "in the coming hours".
The concluding match of the tour at the SCG begins on Sunday, 4 January.
England have already lost key quicks Mark Wood due to knee trouble and another paceman with an abdominal strain on the current trip.
Matthew Fisher was called up as injury reinforcement.
Atkinson struggled in the opening two Tests, taking just a handful of scalps.
He was omitted of the third Test, before being recalled for the Boxing Day match as Archer's replacement.
Atkinson performed better in the fourth Test, claiming a couple of wickets in Australia's first innings, then making 28 as a batsman being one of only three England players to reach double figures.
Following a brief spell late on the first day, he returned the next day and dismissed the nightwatchman edging to the keeper.
However, at the end of his spell, he delivered a variation to the batsman and immediately felt his left hamstring.
Atkinson was brought back for the fourth Ashes Test having missed of the third.
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