Two fire crews were called to Copthorne Road at about 3.15am on Thursday.
Shropshire Fire and Rescue Service said that no-one had been trapped and crews made two vehicles safe.
The ambulance service and police also attended.
Claire Brown, spokeswoman for West Midlands Ambulance Service, said: "We were called to reports of an overturned car on Copthorne Road, Shrewsbury at 3.17am.
"Two ambulances and a paramedic officer attended.
"Crews arrived to find three occupants out of the car.
"The driver, a woman, was assessed and discharged into the care of the police.
"Two men, both passengers, were given treatment on scene for injuries.
"One was taken to Princess Royal Hospital with minor injuries and the second was conveyed to Royal Shrewsbury Hospital with more serious injuries."