Acting on a tip, authorities obtained a warrant and arrived at Onyemata's apartment, where they said they discovered "marijuana, cannabis oil, marijuana edibles and hemp powder."
Onyemata received a misdemeanor citation and is due in court at a date to be determined.
Underhill and Vargas noted an arrest for marijuana possession can carry a four-game suspension from the NFL.
The Saints selected Onyemata in the fourth round of the 2016 draft, and he has appeared in every one of the team's games over the past three seasons. He finished 2018 with 35 combined tackles and 4.5 sacks, with the latter number tied for fourth-highest on the team.
Onyemata helped the Saints defensive line finish second in adjusted line yards and fourth in adjusted sack rate, per Football Outsiders. The unit sat 17th and sixth, respectively, in those two categories in 2017.
Sheldon Rankins tore his Achilles in New Orleans' NFC Divisional Round win over the Philadelphia Eagles, which could jeopardize his availability for the start of the 2019 season.
If the NFL suspends Onyemata, the Saints might be down their two best interior defenders to open the year.