Lee pulled up in the early stages of the second quarter after a run play and didn't return.
"I don't know the severity, but obviously it's not good," Lee said. "So, we got to figure it out and do whatever I can to rehab and get back as fast as possible."
Lee, who leads the Cowboys with 90 tackles on the season, was replaced by Justin Durant in the base defense. But Durant left the game with a hamstring injury, leaving the Cowboys with Ernie Sims, Kyle Bosworth and Cameron Lawrence as the fill-ins.
Hatcher, who has not been cleared to play by the doctors, said he expects to return after the Cowboys' bye week.
"I'm more than sure," Hatcher said. "I'm going to get in the weight room and I won't have a bye week and I want to come back being the Jason Hatcher I left and helped my team win. It hurt me not being out there [Sunday]."
Also, wide receiver Dwayne Harris left the game in the first quarter with neck and shoulder injuries after getting pushed out of bounds during a kickoff. Harris did return.
Running back Phillip Tanner left the game with cramps.