Scientists found a pattern of diminished brain volume in those with a variant of the gene known as FTO.
The mutation can cause people to over-eat and is carried by almost half of Caucasians but only 16 percent of Asians, which could help explain why they suffer less from obesity.
Neurologist Professor Paul Thompson and colleagues said the brain differences could not be directly attributed to other obesity-related factors such as cholesterol levels, diabetes or high blood pressure.
Obesity increases the risk of dementia because it can lead to damage of the blood vessels in the brain, which in turn leads to the death of brain cells.
The study, published in Proceedings of the National Academy of Sciences, did not identify the mechanism behind the brain damage and cannot determine where the faulty gene's influence on obesity lies.
But thoes with the mutation had at least eight percent fewer cells in the frontal lobes of the brain - the part most involved in complex judgements - and 12 percent less in the occipital lobes which is associated with the processing of mental imagery. These areas also showed damage in subjects with higher body mass index (BMI).