The trio played just three Tests between them during the home Ashes series, with Hazlewood missing from Australia's Test side since July 2025.
Their returns - alongside the selections of seamers Mitchell Starc and Scott Boland - could create a selection headache for Baggy Greens' head coach Andrew McDonald, with Boland taking 20 wickets in the series against England as Australia won the series 4-1.
"Scotty would never say it, but I think he's mounting a strong case that when you use the words of big three (fast bowlers), that he could be one of those," Australia's chief selector George Bailey said.
The returns of Hazlewood and Cummins mean that Michael Neser misses out despite taking 15 wickets in the winter Ashes series.
The squad does see a return for opener Jake Weatherald though, who has looked in fine fettle for Leicestershire in the County Championship, scoring 483 runs at an average of 60.37. Weatherald, 31, could open the batting for Australia in his home town if selected for the first Test in Darwin, starting on August 13.
Warwickshire overseas player Beau Webster also provides an all-round option for Australia in the middle order, with Cameron Green also looking to make an impact after a disappointing Ashes series with both bat and ball.
Australia's two-Test series against Bangladesh, with the second Test being played in the Queensland town of Mackay, will provide preparation for a formidable three-Test tour of South Africa to come in October.
Australia 13-man squad vs Bangladesh:
Pat Cummins (captain), Scott Boland, Alex Carey, Cameron Green, Josh Hazlewood, Travis Head, Josh Inglis, Marnus Labuschagne, Nathan Lyon, Steve Smith, Mitchell Starc, Jake Weatherald, Beau Webster.
