The incident happened around 2am yesterday (Sunday) on the A199 Haddington to Dunbar Road, near to the junction with Over Hailes Farm in East Linton.
An orange Daewoo Matiz was travelling west along the road when the 21-year-old female driver lost control of the vehicle.
The car then crossed the roadway and mounted the verge on the opposite side before colliding with a wall and overturning.
Police and ambulance service attended and the driver and another 21-year-old woman, who was a passenger, were taken to the ERI after sustaining non life-threatening neck, back and arm injuries.
Officers are asking any motorists who were on the road at the time and witnessed the collision to come forward.
A police spokesman said:
Both women were incredibly fortunate to escape from the vehicle without serious injury and we are now carrying out a full investigation to determine the circumstances surrounding this incident.
Anyone who can assist with our enquiries is asked to contact police immediately.
Those with information can contact: