It is Irving's third suspension in three seasons. He will be a free agent when the league year begins, and the Cowboys have not expressed a desire to bring him back.
Irving was suspended for the first four games of both the 2017 and '18 seasons for violating the substance abuse and personal conduct policies.
Earlier this week, Irving posted a message on Instagram, explaining why he is in the NFL.
"I'm in the NFl [sic] because I'm great at what I do," Irving wrote. "I'm not in the NFL because I'm an Eagle Scout, or the perfect model citizen. I didn't put on a mask or kiss ass to be where I am. I'm here on natural ability. This is God's plan. Not mine. Trust me, I'm adjusting to it as well. Once I step on the field and stop performing, THEN we have a problem ... So does anyone have anything to say about my play?"
ESPN's Todd Archer and Adam Schefter contributed to this report.