He was believed to be travelling to Leeds from his home town of Crewe.
Club officials have so far refused to comment but West Yorkshire Police say they are still questioning a man.
A police spokesman said: "A 24-year-old Wetherby man was arrested on the M62 Chain Bar Roundabout shortly after midnight today [Thursday].
"He will be questioned by police later."
Johnson moved to Leeds from Derby County in October 2001.
But a string of injuries have restricted him to just 28 appearances.
Eirik Bakke was convicted for drink driving last year and banned for two years.