Police closed Wombridge Road outside the Co-op in the Trench area after the incident, which took place shortly before 9.40am.
The ambulance service were also sent to the scene, with one witness saying there had been a bus at the bus stop when the crash happened.
They said a black Ford Fiesta had mounted the kerb and had crashed into the bus stop, hitting a woman and a pram carrying a child. She was taken to hospital with injuries "not believed to be life-threatening".
The young girl's father has since said she is fine and praised passing student nurses who helped at the scene.
Photos from the crash show the Fiesta with damage to the front end and both front airbags deployed, with part of the pram left next to the hatchback.
It is understood the driver had very recently passed her test. The car had a P plate fixed to its tailgate.
A spokeswoman for West Midlands Ambulance service said: "We were called at 9am to reports of an RTC involving a car and pram on Wombridge Road. We sent one ambulance and a paramedic officer to the scene. Crews have treated a young girl for injuries not believed to be life-threatening and she’s been conveyed to hospital for further treatment.”
Newport Police confirmed the road had been closed, writing on Twitter: "Wombridge Road closed between Richmond Avenue and Teagues Crescent due to RTC. Please avoid the area. PCSO Collumbell assisting with traffic control."
West Mercia Police said: "Police were called to Wombridge Road in Telford at 9am this morning following reports of a collision.
"A vehicle struck a bus stop, which resulted in a child being injured. The child was taken to hospital by ambulance but their injuries are not believed to be serious.
"There may be disruption in the area for some time as repair work takes place to make the bus stop safe."