Hardie suffered an injury to his left shoulder while training with Western Australia last Friday, and has since been withdrawn from the multi-format tour.
Will Sutherland has been called up in Hardie's place, but won't arrive in India until after the first of two four-day games starting next week.
Hardie is hopeful of returning for WA during the early rounds of the Sheffield Shield, with the injury not believed to be season-destroying.
But it is still the latest in a long line of injuries for quicks ahead of the summer.
Speedster Lance Morris and Queensland youngster Callum Vidler have both been ruled out of the A tour in India after suffering back injuries.
Morris will require surgery on his back, with his summer already over and any chances of a Test debut in the Ashes officially gone.
Jhye Richardson (shoulder) is also no certainty to be available before the start of the Ashes, while fellow West Australian Mahli Beardman is also nursing a stress fracture.
Pat Cummins is currently sidelined by highly-publicised back issues, with the Test captain hopeful of being back bowling at least a month out from the first Test on November 21.
Australia have arguably the best pace-bowling quartet in world cricket with Cummins, Mitchell Starc, Josh Hazlewood and back-up quick Scott Boland.
But below them, depth is looking increasingly concerning if things were to go awry during the Ashes.
"We feel really well placed," Cummins insisted earlier this week.
"A lot of planning goes in. It's not just a month before, it's 12 months out.
"Someone like Jhye Richardson hopefully he will be available for some of the summer.
"There's (Michael) Neser, Brendan Doggett was part of squads last year, Sean Abbott. So I'm really confident in our depth.
"Obviously there is a bit of Shield cricket and white-ball cricket before that to make sure everyone is up and raring to go."
Australia A will start their first four-day game against India in Lucknow next Tuesday, before another a week later.
Three 50-over games will follow in Kanpur on September 30, October 3 and October 5.
Sam Konstas and Nathan McSweeney headline the Test hopefuls in the four-day squad, with the duo to feature in the red-ball games before returning home for the Sheffield Shield.
Selectors have made clear the tour is more about preparing for the five Tests in India in 2027 than the looming home Ashes.
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