The Vikings said Peterson wouldn't travel with the team as he misses just the fourth game of his five-year NFL career.
Vikings coach Leslie Frazier said Peterson was out of his walking boot on Thursday and made progress by working on the side at practice Friday but still wasn't able to plant his foot or make a cut well enough to play. Peterson had been listed as doubtful because of ligament damage in his left ankle.
Peterson is sixth in the NFL in rushing with 872 yards. He's tied with Philadelphia's LeSean McCoy with a league-leading 12 touchdowns.
Safety Husain Abdullah (concussion) and right guard Anthony Herrera (left knee) were also declared out for Sunday's game.
Tight end Kyle Rudolph missed practice all week with a quadriceps contusion and is listed as doubtful. Harvin (ribs) and tight end Visanthe Shiancoe (hamstring) are listed as questionable after practicing on a limited basis Friday. With their top two tight ends hobbled, the Vikings signed tight end Allen Reisner from the practice squad Saturday and waived wide receiver Stephen Burton.
The Associated Press contributed to this report.