The 71-year-old was crushed under the vehicle as she crossed Princes Street opposite the Waverley Steps and beside the Balmoral Hotel on Thursday.
The crash happened at about 12:15 and the road was closed for two hours.
Sgt Iain Blain, of Police Scotland, said: "This collision has left a woman with serious injuries and we are keen to hear from anyone who witnessed it."
A woman who was knocked down by a taxi in Edinburgh city centre is in hospital with multiple serious injuries.