'Major setback' for the touring side after Atkinson goes off with a hamstring injury.
The pace bowler added to the injury concerns plaguing England when he left the ground early on day two in the Melbourne Test against Australia.
The pace bowler experienced discomfort in his left leg immediately following a delivery in his spell on Saturday.
The England team stated Atkinson had experienced "tightness" and required time off the field for further assessment "during the day".
The concluding match in this Ashes battle in Sydney starts on Sunday, 4 January.
England have been without fast bowlers Mark Wood to a knee injury and another paceman with an abdominal strain on the current trip.
Matthew Fisher was called up as cover for Wood.
His form was underwhelming in the opening two Tests, taking just three wickets.
He was dropped for the Adelaide match, then recalled for the fourth Test in the playing XI.
Atkinson performed better in the fourth Test, claiming a couple of wickets with the ball, before adding 28 while batting being one of only three teammates to reach double figures.
Following a brief spell at the end of day one, he returned for the second day's play and dismissed the nightwatchman Scott Boland caught behind.
However, towards the conclusion of that over, he bowled a change of pace to Travis Head and promptly felt his left hamstring.
Atkinson returned to the side for the Boxing Day Test having missed the previous Test.