Peterson, 31, suffered a torn meniscus on Sunday, just two games into his 10th pro season.
Jerick McKinnon and Matt Asiata filled the void in 2014 when Peterson missed all but one game, and are expected to do the same moving forward. Zimmer said McKinnon is likely to start against the Panthers on Sunday.
The Vikings also signed veteran free agent Ronnie Hillman on Wednesday.
Peterson underwent successful surgery on his right knee on Thursday.
The Vikings have not exercised the one “designated-to-return” option on a player on injured reserve, but Peterson and Matt Kalil would be eligible for that option later this season.