The paceman's availability had been in doubt for weeks because of a back injury, and Cricket Australia confirmed the inevitable on Monday morning.
Steve Smith will be captain in his absence.
It is the first of several big selection calls for the Australian team ahead of the first Test from November 21 at Perth's Optus Stadium.
The top order is a work in progress, with a partner for opener Usman Khawaja to be confirmed, and allrounder Cameron Green is yet to prove his fitness.
But confirmation of Cummins' unavailability means Victorian Scott Boland is a lock to join Mitchell Starc and Josh Hazlewood as the pace attack for Perth, with Nathan Lyon the spin bowler.
Cummins' injury is a major blow for Australia's hopes of retaining the Ashes. Coach Andrew McDonald will hold a media conference on Monday afternoon in Canberra amid uncertainty over when Cummins will return to the Test side.
"Cummins has resumed running and expects to return to bowling shortly," a Cricket Australia spokesman said.
Smith, 36, is back in Australia after six weeks in New York. He will play for NSW in two Sheffield Shield matches before the first Test.
He said last week he is more relaxed than when he was the full-time captain between 2013 and 2017.
And he also knows his batting improves with the role, averaging 68.98 in the role compared with 49.90 when not captain.
"It's interesting how the brain works," Smith said.
"I feel like I kind of go to another level and try to set a standard, I suppose."
While fellow batsman Marnus Labuschagne has firmed for a Test recall with a run of strong early-season domestic form, young opener Sam Konstas has dropped down the pecking order after several low scores.Â
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