Vice-captain Warner suffered a broken thumb when struck by a Steven Finn delivery in the second one-day international against England and does not expect to pick up a bat for six weeks.
Australia, who already lost opener Chris Rogers to retirement after the Ashes, meet Bangladesh in the first test in Chittagong starting Oct. 9 followed by the second in Mirpur from Oct. 17.
Warner previously broke the same thumb in 2013 and recovered in a few weeks to be able to tour India but said his latest injury was more serious.
"I knew pretty much straight away when I got hit that it was the same one and it was quite painful," Warner told reporters before flying home to Australia.
"Look I know from last time when it was actually just a minor fracture, it was a minimum of three weeks before I could pick up a bat... I never do want to miss a Test match but it's probably highly unlikely I'm going to make Bangladesh.
"I'm gutted. I'm not happy about that but I'll get a bit of a break now and have got six to eight weeks off before we have to come back and assemble for the first-class game in Adelaide so it's now time to get back as soon as possible and then I can work on my fitness for longevity for the next few years."
Rogers joined former captain Michael Clarke in retirement after the Ashes, with pace bowler Ryan Harris quitting the game after suffering a knee injury in the leadup to the series.
With all-rounder Shane Watson announcing his decision to quit test cricket on Sunday, captain Smith will need to carry a team depleted of experience in his first full series in charge.
Joe Burns, who played two tests against India in the home summer, is considered a frontrunner for one of the opening slots, with Cameron Bancroft and Usman Khawaja also rated contenders after posting big scores on Australia A's tour of India.
With wicketkeeper and former vice captain Brad Haddin also unlikely to return to the side at the age of 37, the test side faces a dearth of leadership as they rebuild after the 3-2 Ashes loss.
Selectors may prefer the more experienced Khawaja, who led Australia A in India and is captain of Sheffield Shield side Queensland, over uncapped 22-year-old Bancroft.
(Reporting by Ian Ransom; Editing by Sudipto Ganguly)
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