Per ESPN.com's Todd Archer, Martin was ruled out for the rest of the game after he appeared to take a helmet to the knee from a Cincinnati defender on a running play in the second quarter.
He will undergo an MRI on Sunday.
"I'm not thinking that Zack is problematic here," Cowboys owner Jerry Jones said, according to Pro Football Talk's Charean Williams. "I just want to say we've got more to gain from [the MRI], but from what we've seen, I'll sleep good tonight on Martin."
Since being drafted 16th overall by the Cowboys in 2014, Martin has been an essential piece of the offensive line. The Notre Dame alum has never missed a start in his NFL career, appearing in 64 straight games heading into this season.
Martin was at risk of ending that streak last season in Week 12 when he suffered a concussion against the Los Angeles Chargers, but he cleared the concussion protocol in time to be back at right guard the following week against the Washington Redskins.
Martin's absence will have a profound impact on Dallas' offense. Quarterback Dak Prescott and running back Ezekiel Elliott are talented enough to overcome the loss of a key offensive lineman, but everything runs smoother with Martin lined up at right guard.
Cowboys head coach Jason Garrett will turn to veteran offensive lineman Joe Looney, who has appeared in every game over the previous two seasons with the team.