Ambulances and firefighters attended the scene on Woodbury Road at around 5.45am this morning.
The driver of the Ford Fiesta, who is in her 40s, got out of her vehicle and was assessed at the scene.
She was later taken to Queen Elizabeth Hospital in Birmingham as a precaution, with her injuries not believed to be serious.
The road was closed while firefighters from Haden Cross and Oldbury made the scene safe.
A West Midlands Ambulance Service spokesman said: "An ambulance attended and the woman got taken as a precaution to Queen Elizabeth Hospital."