Cummins has taken 309 wickets in 71 Tests and has a career average of 21.19 with the ball at the Adelaide Oval.
Australia are also without fast bowler Josh Hazlewood, while Steve Smith has captained the team in Cummins’ absence.
Cummins said selectors considered bringing him to Brisbane but decided it was too risky.
“It felt a little too sharp and it really wasn’t fair to the other players,” he added.
“We thought it didn’t seem like the right test match to take that risk, so put it to the wayside for a week.”
