Debutant top-order batsman Cameron Bancroft, 22, also gets the nod in a 15-man squad captained by Steve Smith as Australia grapple with wholesale changes.
Ex-skipper Michael Clarke, Brad Haddin, Ryan Harris, Chris Rogers and Shane Watson have all retired as Australia lost the Ashes Test tour but won the one-day series against England 3-2.
Quicks Mitchell Johnson and Josh Hazlewood are both rested after a heavy recent workload, while opening batsman David Warner and leg-spinner Fawad Ahmed are injured.
"The retirements ... As well as issues of injury, form and conditions have brought about a major change in the profile of the touring party from the one that toured the British Isles," said national selector Rodney Marsh.
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"But with that change comes a fantastic opportunity for all the players going to Bangladesh.
"They are going as a young group with seven of the players aged 26 or less, and all 15 have the opportunity to kick on and, in the case of Cameron Bancroft and Andrew Fekete, kick off their Test careers and establish themselves as the core of the side for years to come."
"Cameron is a player who impressed everyone on the recent A tour of India," Marsh said. "He's young, hungry and he could become a very good player for us over a long period of time.
"With Stephen O'Keefe, Nathan Lyon and Glenn Maxwell we believe we have the right number and the right type of spinners for the conditions we expect to encounter.