A West Yorkshire Police officer tweeted the images of the incident which occurred at around 6am on Tuesday morning just before junction 24 westbound.
The officer known on Twitter as Motorway Martin said: "Not quite sure how the driver of this vehicle managed to end up this far up the banking!!"
Another Highways England Traffic officer, Sam Blakeborough said: "The occupants were very lucky it didn't roll over."
No one in the vehicle was injured in the incident.
A further incident on the M62 occurred on Tuesday afternoon.
A vehicle broke down at junction 31 eastbound, near Normanton, causing lane two of the entry slip road to close temporarily.
The lane is expected to reopen between 5pm and 5.15pm.