The red car, a Mercedes, sustained extensive damage but the driver escaped serious injury, said West Midlands Ambulance Service.
The crash took place on Castlecroft Road just after 6am today.
A spokesman for West Midlands Ambulance Service said: "We were called to reports of a collision between a car and a lorry on Castlecroft Avenue at 5.58am, one ambulance and a paramedic officer attended the scene.
"On arrival we discovered one patient, a woman, who was the driver of the car.
"She was treated for injuries not believed to be serious before being taken to New Cross Hospital for further assessment."
Several roads in the area were also closed with motorists warned to find alternative routes.
Police and firefighters were also at the scene.