"We have been closely monitoring his recovery since that match but feel he has not fully recovered," team physio Alex Kountouris said in a statement on Sunday. "He will not play in the upcoming Sydney test match.
"We expect him to recover in time to play a part in the upcoming tri-series against England and India."
The rescheduled fourth test begins on Jan. 6 before the international tri-series starts 12 days later.
With the 50-over World Cup coming up in February, coach Darren Lehmann said Australia decided to err on the side of caution with Johnson.
"Mitchell is an important part of our plans for the remainder of our summer and we want him 100 percent right so won't be taking any risks with him," Lehmann explained.
"We believe it is best for Mitchell to take this opportunity to freshen up and get his body fully fit ahead of the tri-series."
Mitchell Starc is expected to replace Johnson in the test squad.
(Reporting by Greg Stutchbury, editing by Tony Jimenez)
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