Emergency services were called to the scene at the Tesco store in Tidworth just before 2100 GMT on Saturday.
Police said the driver escaped with minor injuries.
Insp Mark Gale said: "The tanker itself had to be righted by a crane which was called to the scene and that took a considerable time."
He added: "Due to the spillage of the liquids we contacted the environmental health service to make them aware as it can have implications on the water course
