Kent Police said no arrests had been made.
A HM Coastguard Romney Marsh spokesperson said: “The dunes at Greatstone in which this vehicle drove over to get to the beach are protected and provide a unique habitat for plants and animals.
“Driving over these dunes and damaging them constitutes a criminal offence.”
This was not the first time a vehicle had been reported driving over the dunes, the coastguard added.
Folkestone and Hythe District Council, which the coastguard says may be involved in the recovery, has been contacted for more information.