Marsh has not fully recovered from the ankle injury that ruled him out of Australia's recent tour of Pakistan. While he is expected to join the squad in Dhaka and begin preparations for the T20I series, he will miss the ODI leg of the tour.
Head, meanwhile, has been granted personal leave and will be unavailable for both the ODI and T20I series against Bangladesh.
Their absence has prompted Australia to retain Matt Short in the squad, while teenage batter Ollie Peake and off-spinner Todd Murphy have also been included.
Murphy replaces Tanveer Sangha, who was ruled out with a hamstring injury.
National selector Tony Dodemaide said Australia had hoped Marsh would be fit for the ODI series but confirmed the all-rounder is still working his way back to full fitness.
He also noted that Head was initially selected for both formats before being granted leave.
With Marsh unavailable, wicketkeeper-batter Josh Inglis will continue to captain Australia in the ODI series, which begins in Dhaka this week.
Australia squad for Bangladesh ODIs: Josh Inglis (c), Xavier Bartlett, Alex Carey, Cooper Connolly, Ben Dwarshuis, Nathan Ellis, Cameron Green, Matthew Kuhnemann, Marnus Labuschagne, Todd Murphy, Oliver Peake, Matthew Renshaw, Liam Scott, Matt Short, Adam Zampa
