A magazine report had claimed that Price, 34, has been speeding past five caravans parked near her mansion, scaring their animals.
"The People put a story to me, said it was not true but they are publishing anyway. Usually I would take rough with the smooth but this story is quite nasty," Price posted on Twitter.
"It suggests I have been anti social to travellers living nearby. Not true! It suggests I complained about them. Not true. My family has traveller genes - an invented story!," she added.