The 41-year-old was walking along Church Way when the incident happened at around 10.05am today.
The collision happened just yards from the pedestrian crossing near Doncaster Minster.
A police spokesman said: “The light goods vehicle is believed to have driven past and the woman’s shopping bags have become caught in one of the wheels. This has then pulled the woman under the back of the vehicle and the LGV has driven off.
The spokesman said the pedestrian’s injuries were “possibly life changing.”
The road is expected to be closed for several hours following the incident while police officers carry out investigations.
Police are appealing for the driver of the LGV who may not even be aware of the incident, to come forward.
Anyone who may have witnessed the incident or who was in the area between 9.55am and 10.10am should also contact police quoting incident number 295 of May 23.
The LGV is described as a white Volvo with a blue curtain sided trailer.