Martin returned to the field after he was looked at for a shoulder stinger in the first quarter, but he went down again and had to be helped off the field by team medical staff.
The four-time All-Pro was one of the last pieces standing on the Cowboys offensive line, which has been depleted by injuries. La'el Collins is out for the season with a hip injury, while Tyron Smith was ruled out before Week 5 after undergoing neck surgery.
With Martin out, the Cowboys turned to 2019 third-round pick Connor McGovern, who entered Monday having played two offensive snaps in his career. He joined undrafted free agents Brandon Knight and Terence Steele alongside 2018 second-round pick Connor Williams and this year's fourth-round pick Tyler Biadasz in protecting Dak Prescott fill-in Andy Dalton and the rest of the Cowboys offense.
The Cowboys scored a season-worst three points in the first half and trailed the Cardinals 28-3 with three minutes remaining in the third quarter.