Batsmen Travis Head and Peter Handscomb were preferred to Marsh, while Marcus Harris will make his debut as an opening batsman.
Tim Paine said Marsh's omission was due to a lack of consistency in his performances and he would benefit from returning to Sheffield Shield cricket to get in runs again.
Handscomb edged him out after two half-centuries last week and a century for Victoria the week before that.
"Mitch Marsh has not been as consistent as he would like and we would like," said Paine at his pre-match press conference.
"We know the talent that Mitch has and we know that most likely at some stage in this series we will need him.
"We are taking the opportunity at the moment to go back and play a Shield game and get some cricket under belt."
Debutant Harris will open the innings alongside Aaron Finch, with Khawaja, whose brother was arrested for allegedly framing a colleague with a fake terror plot, coming in at third place.
Khawaja, who is returning after ankle surgery, was not seen in the nets on Wednesday after his family crisis, although he is known to only take on a light workload the day before a Test.
Shaun Marsh will bat at four with Handscomb at five and Head at six.
The axing of Mitch Marsh will add an extra load on Josh Hazlewood, Mitchell Starc, Pat Cummins and spinner Nathan Lyon, who will have to take on more overs in scorching hot conditions in Adelaide.
"We obviously have a lot of confidence in Nathan Lyon bowling a lot of overs if we need to," said Paine.
"And probably the fact that all our three quicks go in real fresh. We have confidence in them, particularly at the start of the series."
Marcus Harris, Aaron Finch, Usman Khawaja, Shaun Marsh, Travis Head, Peter Handscomb, Tim Paine (capt), Josh Hazlewood, Pat Cummins, Nathan Lyon, Mitchell Starc