Peterson will miss at least the Vikings' next three games with the move. Coach Mike Zimmer said he doesn't believe the eight-time Pro Bowl selection's injury would end his season.
Peterson left the Vikings' 34-28 overtime victory over the Carolina Panthers late in the fourth quarter because of cramping after defending against DJ Moore on a pass that fell incomplete. He didn't return for the overtime period.
Peterson was replaced in the game by Cameron Dantzler, who presumably would fill Peterson's role in the starting lineup while he is on IR.
Asked how he feels about the rest of his cornerback group in Peterson's absence, Zimmer said: "I feel fine. Patrick's played really well. We'll miss him for sure, but Dantzler's done decent and so has [Bashaud] Breeland."
Peterson signed with the Vikings this offseason after spending the first 10 seasons of his career with the Arizona Cardinals.
The Vikings improved to 3-3 with their victory Sunday.
ESPN's Courtney Cronin contributed to this report.