The squad, captained by George Bailey, also has wicketkeeper Brad Haddin. If Hogg plays in the tournament, he will become the oldest cricketer in international T20s.
Both Hogg and Hodge have been rewarded for their performances in the Big Bash League (BBL).
Commenting on the squad, National Selector John Inverarity said: "We have selected a squad that has plenty of experience playing the Twenty20 format in the sub-continent, which augers well for the challenges of Bangladesh," Inverarity said.
"Brad Hogg comes into the squad as the other frontline spinner. Once again Brad bowled very well for the Perth Scorchers in the Big Bash League and many batsmen found him difficult to read. Despite his age, his enthusiasm and fitness are undiminished.
"Glenn Maxwell and Dan Christian provide good all-round capabilities including important bowling variety and excellent fielding.
"Brad Hodge has made a great number of Twenty20 runs on the sub-continent and played many match defining innings there. He will provide the squad with a great deal of calm experience and knowledge. His inclusion is just reward for his outstanding performances in this form of the game over many seasons," he added.
Australia Squad: George Bailey (captain), Dan Christian, Nathan Coulter-Nile, James Faulkner, Aaron Finch, Brad Haddin, Brad Hodge, Brad Hogg, Glenn Maxwell, James Muirhead, Mitchell Johnson, Mitchell Starc, David Warner, Shane Watson, Cameron White.
Australia's Fixtures at World T20 (Group 2)
Sunday 23 March: Vs Pakistan, Sher-e-Bangla National Cricket Stadium, Mirpur
Friday 28 March: Vs West Indies, Sher-e-Bangla National Cricket Stadium, Mirpur
Monday 31 March: Vs India, Sher-e-Bangla National Cricket Stadium, Mirpur.
Tuesday 1 April: Vs Qualifier, Sher-e-Bangla National Cricket Stadium, Mirpur.