Emergency services initially feared the man was trapped, but when they arrived they discovered him outside the vehicle with only minor injuries.
A Scottish Ambulance Service spokesman said: "The man, in his late 30s, was taken to the Edinburgh Royal Infirmary suffering from minor injuries."
One worker at the scene said: "The guy's been reversing and he's misjudged the weight of the vehicle. The driver has been taken to hospital but he's ok."
John Jack, director of facilities at NHS Lothian, said: "A delivery driver was taken to hospital, as a precaution, after an accident in the grounds of the Western General Hospital.
"There is no interruption to patient care and health and safety inspectors are currently assessing the incident."