Cardinals coach Bruce Arians said that the team wouldn't know Palmer's prognosis until more tests are done.
"We don't know anything about Carson's injury or the length or whatever it is yet," Arians said following Arizona's 31-14 victory. "It is obviously a knee, but he will be evaluated and get an MRI and everything, and we'll know something more hopefully by Tuesday."
Arians is scheduled to address the media again Monday afternoon.
Palmer was injured on a sack by Rams safety Mark Barron with about 11:21 left in the fourth quarter Sunday, just two days after he signed a three-year contract extension worth a reported $50 million, including $20.5 million guaranteed.
Barron hit Palmer but didn't bring him down. However, Palmer went to the turf a moment later and lay on the field while he was attended to by team trainers and doctor. While he was walking off the field, he appeared to stumble and had to be held up. He was then carted off the field.
Palmer was 25-for-36 passing for 241 yards and an interception before the injury. He missed three games earlier this season with a damaged nerve in his throwing shoulder. The Cardinals won two of those three games with Drew Stanton starting at quarterback.
Stanton replaced Palmer on Sunday, leading the first-place Cardinals (8-1) to their fifth straight victory.
"We knew Drew would come in and do a heck of a job," Arians said.
Palmer tore the ACL and MCL in the same knee during the playoffs in 2006. His surgeon at that time deemed the damage a "four" on a "scale of one to three."
The last time Palmer suffered a similar knee injury, he signed a six-year, $118 million contract on Dec. 29, 2005 -- just 10 days before tearing his ACL and MCL.
ESPN.com Cardinals reporter Josh Weinfuss and The Associated Press contributed to this report.