NFL Network Insider Ian Rapoport reported Thursday that Woods was arrested on Tuesday at a traffic stop and charged with possession of marijuana over two ounces but less than four ounces, tampering with evidence, and cited for possession of paraphernalia, according to the Frisco Police Department.
Woods could be subject to punishment under the league's personal conduct policy.
The arrest is the latest setback for Woods, who has struggled to stay healthy in 2019. The 26-year-old missed last week's game with a knee injury and was already ruled out of Thursday night's matchup with the Chicago Bears due to the injury.
NFL Network's Stacey Dales reported Cowboys coach Jason Garrett has spoken with Woods and has informed him he wouldn't make the trip to Chicago.
After going undrafted out of USC in 2016, Woods spent two seasons in Tennessee, mostly on the practice squad. The DT signed a two-year deal in Dallas last offseason, and compiled 34 tackles, 1.5 sacks and one pass defended in 15 games in 2018. This season he has played in just eight tilts while battling injury, earning 15 tackles and no sacks.