Coach Jason Garrett didn't elaborate on the linebacker's condition when asked about his status at Monday's news conference.
"We don't want to get into the specifics of Sean other than to say he has a serious knee injury, he's in the process of rehabbing right now and we're coming up with a plan for him going forward," Garrett said.
The Cowboys current plan is to replace Lee -- their most vital defender -- with an in-house group of veterans and draft picks.
"Justin Durant did work at the mike linebacker position; we have a number of different mike linebacker and other linebacker candidates," Garrett said. "So we're going to give guys opportunities to show us what they can do and see who rises to the top."
One draft pick with a chance to win starting snaps is fourth-round selection Anthony Hitchens. The 6-foot-1, 233-pound linebacker signed his rookie contract Monday, the team announced.
"We drafted a couple linebackers and feel like we have more guys to start with than we did last year at this time," Garret said. "And so we feel good about that. We want to make sure those guys get an opportunity to show us what they can do. And ultimately what we're trying to do is find the best three linebackers. So we'll give them a chance to do what they can do. We'll think about what spots fit them best, fit our team best and make the best decision."
Critics were skeptical when the Cowboys selected Hitchens in the fourth round, as many had him rated as a sixth- or seventh-round selection.