The 55-year-old unnamed suspect passed within feet of the vice president's motorcade on Interstate 94.
Sheriff's deputies trailing the motorcade stopped the vehicle and took the driver into custody after he performed poorly on field sobriety tests.
Officers found an open container of alcohol in the vehicle, Milwaukee County Sheriff spokesperson James Burnett said.
The man allegedly told deputies that he was travelling home after a night out and had no idea that he was driving the wrong way on the road, Burnett added.