Police have received reports of the scam in the New Forest area and have advised motorists to avoid driving through any floodwater in order to avoid the attention of the fraudsters.
Hampshire Constabulary took to its Facebook page to warn residents about the hoax, saying: "Flooding seems to be bringing out the worst in some people.
"We have had two reports this evening of a scam developing in the New Forest whereby someone is moving the 'road closed' signs, and then offering to tow people out with their 4x4 vehicle for a charge of at least �30."
The police appealed for further information and warned: "This is another scam, unfortunately. The simplest and easiest way to avoid it is to not drive into floodwater."
It follows a separate incident in Portsmouth where hoaxers have been cold-calling residents, claiming to be from the National Flood Warning Service. The fraudsters then advise residents to consider evacuating homes because of the impending floods.
Hampshire Constabulary said: "These calls are a hoax. If you are required to evacuate your property in any area in Hampshire and the Isle of Wight, you will receive a personal visit from a uniformed police officer or fire officer.
"Please rest assured and if you get such a telephone call - hang up and ignore it."