Lee was helped off the field by medical personnel, having injured his left knee during a collision with first-round Draft pick Zack Martin.
The 27-year-old underwent further exams later in the day, although head coach Jason Garrett admitted that he was still unsure as to the extent of the problem.
The setback is the latest in a growing list of fitness troubles for Lee, who has missed 16 games over the past three seasons due to an array of injuries.
Five of those matches came last year thanks to a mixture of neck and hamstring injuries, while he also missed 10 games in 2012 courtesy of a toe problem.
The former second-round Draft pick recorded 93 tackles before his injury last season, giving him the third-highest total in the league at that point.