The 26-year-old was arrested and cited for marijuana possession in January.
According to ESPN's Michael Triplett, the Jefferson Parish Sheriff's Office in Louisiana conducted a search of Onyemata's apartment in January after a package to be delivered to the residence was red-flagged. Authorities discovered marijuana, THC oil, edibles and hemp powder on the property.
He was arrested on a misdemeanor charge.
A fourth-round pick in 2016, Onyemata has spent the first three years of his professional career in New Orleans. He is coming off his most productive season to date, recording 35 tackles, 4.5 sacks and one forced fumble in 2018. He was part of a unit that ranked second in the NFL against the run.
The one-game suspension will cause him to miss a regular-season game for the first time in his career. He had appeared in all 48 games since entering the league.