The Toyota Aygo came off the road known locally as Todwick Bends just after 6am.
A 52-year-old woman was treated at the scene by paramedics.
The road was re-opened about 7.45am and the vehicle will be recovered later today.
Car ends up in ditch on A57
PART of the A57 was closed this morning after a car left the road and ended up on its side in a ditch.