NFL Network Insider Ian Rapoport reported the pass rusher was suspended four games for violating the NFL's policy on substances of abuse, according to sources informed of the situation.
The team later announced the suspension.
Irving is eligible to participate in all offseason practices and preseason games. He can return to the active roster on Oct. 1.
Irving was suspended four games to start last season for failing the NFL's performance-enhancing drug policy.
The news is that latest stumbling block for the 24-year-old defensive lineman. Irving returned to the Cowboys for mandatory minicamp this week after dealing with a domestic violence allegation when his girlfriend hacked his Twitter account in April. The woman since recanted. Frisco Police closed the case on Irving last month, Rapoport reported.
An impressive pass rusher, Irving earned seven sacks in just eight games in 2017. He sat out the final four tilts due to a concussion issue.
The four-game suspension is a blow the Cowboys defensive line heading into the 2018 season. Irving signed a $2.91 million restricted free-agent tender in April.