Police Sergeant Andrew Duncan says Arizona's limit is point-08 percent.
Johnson was arrested after officers pulled him over for driving 40 miles per hour in a 25 miles per hour zone.
Johnson was released by the Bears three days after his arrest. The team said it was "upset and embarrassed" by the defensive tackle's legal troubles.
Johnson had already had been suspended for the first eight games of next season for violating probation on a gun charge.