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 side in Cummins’ absence.
Cummins said the selectors considered bringing him in for Brisbane but decided it was too risky.
“It felt a bit too acute and didn’t really feel fair on the other bowlers,” he added.
“We thought it didn’t feel like the right Test match to take that risk, so kick it down the road for a week.”