Head coach Bruce Arians confirmed the injury to reporters after Arizona's loss, adding the quarterback would undergo surgery and miss eight weeks.
Palmer exited in the first half, leaving Drew Stanton in charge under center.
The veteran was 10-of-18 for 122 yards with an interception, which he tossed with Arizona down 6-0 in the second quarter. Palmer was hurt on the play, and Los Angeles extended its lead to 13-0 with a touchdown and extra point on the next two snaps.
The Rams went on to win 33-0.
Palmer has endured an up-and-down stay with the Cardinals since arriving ahead of the 2013 season. Arizona likely expected more from the 37-year-old veteran last year after he posted career-best numbers during the 2015 campaign. He's still a vital cog in the team's offensive attack, though.
This setback is a serious concern for the Cardinals, who have failed to address the backup quarterback situation in recent years. Stanton figures to be the next man up for the Cardinals, with Blaine Gabbert behind him.
The Arizona offense figures to struggle with either at the helm. That's why Palmer's status is so crucial to the Cards' chances. The situation should also once again show why the front office must look to find a more reliable backup.
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