Sources told ESPN that the NFL was evaluating Irving for a potential suspension Tuesday. Irving's ban comes two days after the league suspended teammate Randy Gregory for also violating the NFL's substance abuse policy.
Irving was an impending free agent. Sources told the NFL Network that the Cowboys had no intention of re-signing the defensive lineman.
It is the third suspension of Irving's career. The 25-year-old defender was banned for the first four games of the 2017 and 2018 seasons.
Irving played in only two games last season due to his suspension and ankle problems. He tallied four tackles and one sack.
The Kansas City Chiefs originally signed Irving as an undrafted free agent in 2015 out of Iowa State. The Chiefs later signed him to the practice squad, and the Dallas Cowboys signed him away Sept. 29, 2015.
In four seasons with the Cowboys, Irving has 56 total tackles, 12.5 sacks and 12 passes defensed.