Montgomery has not been with the team for any of their practices this week.
Defensive quality control coach Wendel Davis, inside linebackers coach Kirk Olivadotti and outside linebackers coach Mike Smith will help with the defensive line, the team announced Saturday.
The NFL does not believe Montgomery's case is related to any close contacts with the Saints, who have had several cases since Sunday's game against Green Bay.
"They emailed us and told us who those people could potentially be," Packers coach Matt LaFleur said earlier this week. "There was no high-risk close contacts based on what the league told us."
This is the first time this season that the Packers have been without any of their coaches, all of whom are vaccinated.