"He will be evaluated as the week goes along," Cowboys owner Jerry Jones said on 105.3 The Fan. "He's young, he might be able to move on it."
Todd Archer of ESPN noted Woods was injured during the final defensive series of Dallas' 31-21 victory over Washington in Week 2.
A sixth-round pick in 2017, Woods has been a full-time starter since the start of the 2018 campaign. Last year, he established new career highs in tackles (56), pass breakups (nine), interceptions (two) and forced fumbles (one).
Through two games this season, he has 17 tackles and one forced fumble.
Losing Woods will be a tough blow for a Dallas defense that ranks 21st against the pass, allowing an average of 263.5 passing yards per game. Then again, the Cowboys' offense, which is averaging 33 points per game, has forced teams to play catch-up, leading to more pass attempts.
Dallas' upcoming schedule features the likes of the Miami Dolphins, the New Orleans Saints (who will likely be without an injured Drew Brees), the New York Jets and the Philadelphia Eagles.
Fourth-year defensive back Darian Thompson will likely fill in for Woods at free safety.