Pennel played in eight games as a backup in the regular season after joining the Chiefs last season. He started two games in the playoffs and was a reserve in Super Bowl LIV.
The Chiefs were expecting a suspension for Pennel. Defensive coordinator Steve Spagnuolo mentioned recently the team was expecting to start the season without Pennel.
Pennel issued a statement on social media apologizing to the Chiefs and their fans.
"Although I am completely unaware of how this occurred, I take full responsibility for what goes into my body and promise to be more vigilant moving forward," Pennel wrote. "I promise to return with a vengeance in our journey to RunItBack!"
The Chiefs will be without starting cornerback Bashaud Breeland for the first four games of the season, also because of an NFL suspension.