The research, which was published in the American Journal of Clinical Nutrition, studied the effects of both diets on a group of patients suffering from non-alcoholic fatty liver disease (NAFLD).
Dr Jeffrey Browning, lead author of the study, said: "What this study tells us is that if your doctor says that you need to reduce the amount of fat in your liver, you can do something within a month."
He warned that the study was only short term and the "most effective way to reduce liver fat" is to lose weight, no matter what method is employed to do so.
During the study, those on the low-carbohydrate and participants on the low-calorie diet lost an average of ten pounds.
Recent research published in Circulation: Journal of the American Heart Association found that losing excess weight, doing exercise and eating healthy fats could cut blood fat by up to 50 per cent.