Lee pulled up early in the second quarter of the Cowboys' 49-17 defeat with a hamstring problem and did not return to the game after limping off for treatment.
The 26-year-old will undergo an MRI scan later today and he expressed his desire to get back to full fitness as soon as possible.
"I don't know the severity, but obviously it's not good. So, we got to figure it out and do whatever I can to rehab and get back as fast as possible," Lee told reporters.
Lee leads the Cowboys in tackles so far this season with 90 to his name.