Emergency services were called to the Tesco Petrol Station, on Severn Road, at around 12pm on Thursday.
A man and a woman were treated by paramedics for injuries not believed to be serious, before being taken to hospital.
A spokesman for West Midlands Ambulance Service said: "We were called to reports of a collision between a car and a petrol pump at Tesco Petrol Station on Severn Road at 12.03pm on Thursday, one ambulance and a paramedic officer attended the scene.
"On arrival we discovered two patients, a man and a woman. They were both treated for injuries not believed to be serious before being taken to Worcester Royal Hospital on the same ambulance."
A West Mercia Police spokesman added: "Officers were called to reports of a road traffic collision at Tesco, Severn Road, Stourport at just before 12.30pm on November 12.
"The fire service was also in attendance as a precautionary measure."