The 33-year-old reigning ICC Cricketer of the Year's decision to sit out Saturday's session is thought to be precautionary, with an eye on the World Cup starting in Australia next month.
He had warned on Friday he was feeling the strain after taking 13 wickets to help Australia to an unassailable 2-0 series lead ahead of the final test which starts in Sydney on Tuesday.
"Definitely, all us bowlers feel like we need to have a bit of a freshen up," Johnson said, noting the short turnaround before the one-day triangular series with England and India later this month.
"Hopefully I can get a bit of a break at some stage."
Left arm quick Mitchell Starc is the most likely replacement for Johnson should he fail to make it on Tuesday.
(Writing by Patrick Johnston in Singapore)
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