The governing body said "Cummins will not be fit in time" as he recovers from a lower back injury, and that veteran batter Steve Smith would lead the side in his absence.
Australia are clinging to hope the pace spearhead will return later in the five-Test series.
"Cummins has resumed running and expects to return to bowling shortly," Cricket Australia said.
The 32-year-old has not played since picking up a lower back injury in a Test match against the West Indies in July.
Scott Boland looms as the likely replacement, joining fellow quicks Mitchell Starc and Josh Hazlewood.
Australia retained the Ashes in England in 2023 after the series ended in a 2-2 draw.
They beat England 4-0 at home in 2021-22 when Cummins was the leading bowler with 21 wickets at an average of 18.