The Cardinals officially announced the move on Thursday.
Palmer suffered the injury during the second quarter of Arizona's 33-0 loss to the Rams. Head coach Bruce Arians announced after the game Palmer would undergo surgery and miss eight weeks.
Per NFL Network's Ian Rapoport, Palmer's surgery was scheduled for Wednesday and he hoped to return before the eight-week timetable.
By placing Palmer on injured reserve, he will be forced to sit out the full eight weeks. That would make him eligible to return in Week 16 against the New York Giants.
Palmer, who will turn 38 on Dec. 27, is in his fifth season with the Cardinals. He had 1,978 yards, nine touchdowns and seven interceptions in seven games before breaking his arm.
The Cardinals are third in the NFC West with a 3-4 record and are on a bye in Week 8 before playing the San Francisco 49ers at Levi's Stadium on Nov. 5.