Palmer blamed the cramps on the Cardinals' extended time of possession.
"A number of long, long-play drives," Palmer said. "Just a little dehydration, a little cramp."
Palmer completed 23 of 34 passes for 213 yards and a touchdown.
Backup Drew Stanton replaced Palmer with 4 minutes, 20 seconds to play.
Cardinals coach Bruce Arians said he doesn't think the injury is "that severe."
Monday night was Palmer's first game back from a concussion suffered on Oct. 2 against the Los Angeles Rams.
Palmer missed Arizona's win over San Francisco on Oct. 6.
Palmer finds Floyd to increase Cardinals' lead
Carson Palmer throws to Michael Floyd for a 9-yard touchdown, making the score 28-3 Cardinals.