Peterson, who was injured Sunday, told ESPN's Josina Anderson that he has a "bucket handle tear" of the meniscus, which typically has a minimum recovery time of three to four months.
"(I'm) doing it with faith and optimism," Peterson told ESPN of the procedure.
He had been provided with multiple options about how to treat the injury, and he had been waiting to hear back from Dr. James Andrews, who performed extensive surgery on Peterson's knee in 2011, before making his decision.
Peterson slightly twisted his knee at the end of a 5-yard run Sunday against the Packers. His right foot was briefly stuck under the upper leg of Kyler Fackrell as the Packers linebacker brought him to the ground. Peterson left with 3:32 to play in the third quarter.
He hobbled off the field with the assistance of athletic trainers. After being examined on the sideline, Peterson hopped through a field-level club at the team's new stadium toward the Vikings' locker room.
Upon arriving in the locker room, Peterson was quickly ruled out.
He was later seen using crutches with a large black brace around the knee.
He had gained only 19 yards on 12 carries, although his presence had helped Vikings quarterback Sam Bradford hit Stefon Diggs on a pair of long strikes when the Packers were loading up to stop Peterson.
Peterson had a devastating left knee injury in 2011 -- tearing both his ACL and MCL -- only to bounce back and rush for 2,097 yards in the 2012 regular season.
Jerick McKinnon?will be the starting running back and Matt Asiata will serve as the backup against the? Carolina Panthers?on Sunday. The running backs?combined for 1,108 rushing yards in 2014 while Peterson missed 15 games because of NFL discipline.
"I have a lot of confidence in those two guys," Vikings coach Mike Zimmer said Monday. "They're both different types of runners, but I think the combination of the two can help us."
In addition, the Vikings signed free-agent rusher Ronnie Hillman and placed starting left tackle Matt Kalil on injured reserve with a lingering hip injury that will cause him to miss the rest of the 2016 season.
Hillman, who worked out for the San Diego Chargers on Wednesday, started 10 games for the Denver Broncos last season and rushed for a career-high 863 yards and seven touchdowns. He spent four seasons with the Broncos, totaling 1,845 rushing yards.
The injury to Peterson is the latest blow to the Vikings. Quarterback Teddy Bridgewater?tore multiple knee ligaments on Aug. 30, and the team started the season with two different quarterbacks after trading for Bradford on Sept. 3. The Vikings, though, are 2-0 and in sole possession of first place in the NFC North.
"Everything we do is for the team. We're not going to be the only team to have injuries," Zimmer said. "So we're going to keep plugging away."
ESPN's Josina Anderson and Ben Goessling contributed to this report.