Lee, who had an MRI exam Tuesday, is suffering soreness and stiffness, sources told Werder.
But the Cowboys expect that after undergoing treatment to alleviate the symptoms, Lee will be able to play Sunday against the Green Bay Packers, according to sources.
The Cowboys consider Lee as day to day and do not think that the injury is a serious issue, a team source told ESPNDallas.com.
Lee suffered the injury in the third quarter of Monday night's 45-28 loss to the Chicago Bears. He missed the Cowboys' previous two games because of a hamstring injury suffered Nov. 10 against the New Orleans Saints.
Outside linebacker Bruce Carter, who injured his hamstring Monday, also had an MRI and is expected to miss Sunday's game, sources told Werder.
Lee has yet to play a full 16-game season since being drafted by Dallas in 2010.
The 27-year-old Lee missed two games as a rookie with a hamstring injury, one in 2011 with a dislocated wrist and 10 games last season with a toe injury that required surgery.
Dallas signed Lee to a six-year, $42 million extension in the offseason, with a $10 million signing bonus. Some of the money in the future is tied to Lee's playing time in 2013-14.
ESPN.com Cowboys reporter Todd Archer and ESPNDallas.com's Calvin Watkins contributed to this report.