Clady suffered the injury during Sunday's 41-23 victory over the New York Giants. The three-time Pro Bowler's foot was heavily taped following the game, and he was limping badly in the locker room as he exited the training room.
Broncos coach John Fox said Monday that the team is evaluating the injury, which he referred to as a "left foot sprain."
Fox, however, would not confirm whether the sprain was to Clady's Lisfranc.
"I'm not into fortune-telling or tea leaves or any of that good stuff," Fox said. "Right now, it's exactly what I said -- it's a left foot sprain. When we know something, we'll let all the fortune-tellers know."
In what may be a related move, the Broncos signed Clady's backup, Chris Clark, to a two-year extension Monday.
Clark, who was set to become an unrestricted free agent after this season, worked in the left tackle spot throughout offseason workouts, training camp and the majority of the preseason as Clady worked to return from offseason shoulder surgery.
Clady, who signed a five-year deal worth $52.5 million before the season, has started 82 consecutive regular-season games since being drafted by Denver in the first round in 2008.
ESPN's Adam Schefter and ESPN.com's Jeff Legwold contributed to this report.