"Yeah, it's unfortunate," coach Matt LaFleur said Monday. "Certainly Elgton's been a big part of this team and still is a big part of this team, but [he] just won't be out there with us. It's just one of those deals that it's an unfortunate part of our game and we've had a lot of guys unfortunately have to go through this this year."
Jenkins, a Pro Bowl left guard last season, had been filling in for All-Pro left tackle David Bakhtiari, who still has not been cleared to return from last year's ACL injury.
Jenkins suffered the injury to his left knee early in the fourth quarter and was almost immediately ruled out.
Yosh Nijman, the Packers' No. 3 left tackle, will start Sunday when Green Bay hosts the Los Angeles Rams, LaFleur said. Nijman finished the game against the Vikings and held up well in three starts earlier this season when Jenkins missed time because of an ankle injury.
The Packers' plan was that whenever Bakhtiari was cleared to return -- if he comes back this season -- Jenkins would be moved back to left guard.
LaFleur said that Bakhtiari's status will be revisited after the team's bye, which comes after this week.
"We're hopeful that he'll be able to come back this year at some point," he said. "It certainly isn't for a lack of work ethic on his part. It's not for a lack of toughness. It's just one of those things where you never quite know how everybody's going to respond to the recovery process, and I think that's just where we're at with him."
ESPN's Rob Demovsky contributed to this report.