Kris Haskins, deputy mayor of Portland, Dorset, asked to see the pictures taken by the speed camera and discovered that he was only travelling at 14mph.
After challenging the offence, the Dorset Safety Camera Partnership issued an apology, claiming it was a mistake.
The company said a reflected image had caused the camera to react despite Haskins being well under the speed limit.
A spokeswoman for the Dorset Safety Camera Partnership said: 'The partnership concluded that the driver had not committed an offence and no further action would be taken as the camera had projected a reflected image.
'This, although an extremely rare occurrence, triggered the camera's radar, which recorded the vehicle as travelling at 51mph when in fact it was travelling at 14mph.'