Two lanes were closed following the incident which happened during Friday's morning rush hour.
Police say they received a report of the vehicle hitting the central reservation between junctions 35 for Carnforth and 36 for Kirkby Lonsdale.
The car flipped sideways across lanes two and three, but police said that the incident would be moved to the hard shoulder.
Nobody is believed to have been injured in the incident.
Police said the scene was cleared by 9am.