Marshall burst on the scene last season with 1,976 passing yards and 26 total touchdowns, leading Auburn to an SEC title and a berth in the Vizio BCS National Championship.
Malzahn declined to say just how long Marshall would sit against Arkansas.
"I'm not ready to say that yet," he said.
Malzahn said that the inability to start is "part of the punishment."
"The rest is between us," he added.
In addition to Marshall, cornerback Jonathon Mincy will not start Week 1. The three-year starter was arrested and charged with second-degree marijuana possession in late June.
"I will say this: Nick Marshall is still our quarterback and Jonathon Mincy is still our cornerback," Malzahn said.
The coach said both Marshall and Mincy have "responded well."
"Like I said before, my hope is this will help them in the future," he said.
With Marshall out, Auburn will turn to Jeremy Johnson, a 6-foot-5 sophomore from Montgomery, Alabama, who threw for 422 yards, six touchdowns and two interceptions in six games last season.
"Me and Rhett (Lashlee, offensive coordinator) decided Jeremy Johnson will have a bigger role, regardless," Malzahn said. "We feel good about our quarterback position."
The most long-term blow to Auburn, however, was not at the quarterback or cornerback positions.
Alex Kozan, a starter at left guard and an Outland Trophy watch list member, will miss the entire season recovering from back surgery, according to Malzahn.
Auburn To Bench QB Marshall To Start Week 1
Alex Scarborough discusses QB Nick Marshall not starting week 1 for Auburn after being cited by police for marijuana possession.