Martin spent the entire second quarter being evaluated before eventually being ruled out for the night.
The 29-year-old had played in every offensive snap for Dallas through the first five games of the 2020 season.
The six-time Pro Bowler has been one of football's most reliable offensive linemen since the Cowboys selected him in the first round in 2014. He's earned six All-Pro berths and was voted to the NFL's 2010s All-Decade Team.
Dallas has suffered multiple key injuries to its offensive line this season.
The Cowboys allowed three sacks and eight quarterback hits during their 38-10 loss to the Cardinals. Dallas also averaged just 3.6 yards per carry and was held under 100 rushing yards.