The 87-year-old pedestrian was struck at the junction of Stafford Street and St Mary's Street and was then left stuck beneath the vehicle.
Emergency services were called at about 11.15am today.
A police cordon was in place outside Central Square nightclub as investigators took photographs and tried to establish what might have happened.
The fire service were in attendance, as were a number of road ambulances and several police vehicles.
People nearby were in shock as events unfolded. Margaret Wilson, who was shopping in town, said: "There was a lot of noise and commotion. It sounded like the poor lady was in quite a bit of pain.
"It was all quiet one minute and then all these police cars appeared. I hope the lady is going to be alright."
Another shopper said: "There was panic and it became very busy. There were many emergency vehicles. I expect the police will be there a long time."
Concerned passers-by stopped to see what had happened. St Mary's Street was closed but by 12.30pm, traffic was moving as normal in the area.
Claire Brown, spokeswoman for West Midlands Ambulance Service, said an ambulance, paramedic officer and the Midlands Air Ambulance attended.
A doctor, nurse and off-duty member of staff from WMAS were also passing by and stopped to help.
Ms Brown said: "We treated and conveyed one elderly woman who suffered potential serious injuries.
"She was taken by air ambulance to Royal Stoke University Hospital for further emergency treatment."
Police in Telford tweeted that the road would be closed for some time due to a serious road traffic collision.
They are also appealing for witnesses and say the van driver was uninjured.
PC Lewis Carpenter said: “We are looking to speak to anyone who may have witnessed the incident or has any information. We would also like to thank those who were at the scene comforting and caring for the injured lady before emergency services arrived.
“Anyone with any information should call police on the non-emergency 101 number quoting incident reference number 0249s of today.”
Alternatively call Crimestoppers anonymously on 0800 555 111.