According to NFL Network's Ian Rapoport, Irving is facing a four-game suspension stemming from the use of a product he had a marketing deal with.
The 23-year-old Irving signed as an undrafted free agent out of Iowa State with the Kansas City Chiefs in 2015 before the Cowboys signed him off Kansas City's practice squad.
Irving appeared in 12 games as a rookie but took on a far bigger role last season.
He played in 15 games, registering 17 tackles, five passes defended, four forced fumbles and four sacks for the NFC East champions.
Irving was expected to be a key part of Dallas' defensive end rotation in 2017 along with Tyrone Crawford, Demarcus Lawrence and 2017 first-round pick Taco Charlton.