Oliver was taken to the Montgomery County Jail after being pulled over on State Highway 242. Both charges are misdemeanors, according to the jail's website.
The 22-year-old Oliver had an open beer between his legs and was determined to be impaired after a field sobriety test.
The officer who administered the test noted that Oliver may have been impaired by something other than alcohol, and police discovered a pistol in Oliver's vehicle. No drugs were found.
Police were alerted to Oliver's driving by a 911 call from another motorist, who reported a Ford Super Duty pickup hauling a trailer with a dune buggy on it through a 45 mph construction zone on State Highway 242. The 911 caller noted that Oliver was "failing to maintain a lane and driving dangerously."
Oliver underwent a mandatory blood draw before being transported to the jail.
"We are aware of the situation and we are gathering more information," the Bills said in a statement. "We will have no further comment at this point."
The 6-foot-1, 287-pound Oliver was the ninth overall selection in last year's draft and had an immediate impact for the Bills, recording 43 tackles and five sacks last season as a rookie.