Ian Rapoport of NFL Network reports that Palmer is "believed to have torn his ACL" and that the quarterback will have tests to confirm the injury.
Palmer sustained the injury in the fourth quarter of the game. It appeared to be a non-contact injury.
In 2006, Palmer tore his ACL in the same knee he injured Sunday.
The injury occurred two days after Palmer signed a three-year, $50 million contract.
ESPN's Chris Mortensen reported that the contract is only guaranteed through next season and that the average salary ranges between $15.9 million and $16.6 million.
Palmer was replaced in the game by backup quarterback Drew Stanton. The Cardinals, who were losing 14-10 when Palmer left that game, scored three touchdowns after Palmer left. The Cardinals won 31-14.
Stanton completed 3 of 5 passes for 85 yards and a touchdown.
Palmer has played 11 seasons in the NFL and is in the midst of his second with Arizona. He led the team to a 10-6 record last season, its best since 2009. He is 5-0 as a starter this season. He missed three games with a nerve issue in his throwing shoulder.
Entering the game, Palmer was averaging 277 yards per game and had thrown 11 touchdowns and two interceptions this season.
Palmer was the first pick of the 2003 draft out of USC. He was the winner of the 2002 Heisman Trophy.
- Sarah Barshop and Dan Gartland