According to Scott Engle of the Montgomery County Police Reporter, Oliver was pulled over after another driver reported that his Ford Super Duty pickup truck was "failing to maintain a lane and driving dangerously" in a construction zone.
Officers found an open beer between Oliver's legs and after undergoing a field sobriety test, it was determined that Oliver was "impaired but by possibly something besides alcohol."
A pistol was also discovered in Oliver's vehicle.
Oliver was arrested and taken to Montgomery County Jail in Magnolia, Texas.
Buffalo selected Oliver with the No. 9 overall pick in the 2019 NFL draft after he enjoyed a standout collegiate career at the University of Houston.
The 22-year-old had an instant impact as rookie, appearing in all 16 games and making seven starts. He finished his debut campaign with 43 tackles, five sacks, five tackles for loss and one forced fumble.
Oliver put up impressive numbers for a Bills team that reached the playoffs as a wild card in the AFC despite playing 50 percent or fewer of the team's defensive snaps in seven of their 16 regular-season contests.
The Houston native is expected to have an even bigger role in 2020, but his arrest could put him in violation of the NFL's personal conduct policy and subject him to a suspension.
Losing Oliver for any period of time would hurt the Buffalo defense since he is such a skilled pass-rusher up the middle, but Bills general manager Brandon Beane and head coach Sean McDermott did well to build up depth across the defensive line this offseason.
Buffalo added Quinton Jefferson and Vernon Butler to a defensive tackle group that already included Oliver, Star Lotulelei and Harrison Phillips, who is set to return in 2020 after missing the entire 2019 season with a knee injury.
There is also some thought that rookie second-round pick A.J. Epenesa can kick inside from defensive end on passing downs to provide some push and pressure up the middle.
The Bills are well equipped to absorb some temporary losses at defensive tackle, but Oliver is by far the quickest and most explosive player Buffalo has at the position.