"Hailed by experts as keeping people slim, healthy and long-living, the Mediterranean diet has followers all over the world -- but is increasingly disregarded around the Mediterranean," said a statement from the UN body.
Senior FAO economist Josef Schmidhuber said the Mediterranean diet, based on fresh fruit and vegetables, was becoming less popular in several countries in its home region including Greece, Italy, Portugal and Spain.
Growing affluence had changed the eating habits in southern Europe, north Africa and the Near East to the extent that a region once held up as a dietary model was now showing worrying health trends, he noted in a research paper.
They had switched from a diet traditionally light on animal products to more meat and fatty foods. What they now ate was "too fat, too salty and too sweet," Schmidhuber reported.
"Higher calorie intake and lower calorie expenditure have made Greece today the EU member country with the highest average Body Mass Index and the highest prevalence of overweight and obesity," said Schmidhuber.
"Today, three quarters of the Greek population are overweight or obese," he added.
More than half of the Italian, Spanish and Portuguese populations were also overweight, said Schmidhuber.
And there had been a "vast increase" in the overall calories and glycaemic load of the diets in the Near East-North Africa region.
People with a high glycaemic index are more likely to develop health problems such as heart disease and diabetes.
Of 15 European Union nations surveyed, citizens across the EU were ignoring the recommendations of both the FAO and the World Health Organization regarding calory intake.
"But Greece, Italy, Spain, Portugal, Cyprus and Malta, who started out poorer than the northerners, upped their calorie count by 30 percent," said the FAO statement.
For Schmidhuber, the change in eating habits was not just due to higher incomes.
Other factors included the development of supermarkets, working women having less time to cook and families eating out more, often in fast-food restaurants.
And while people were consuming more calories, their lifestyles had become more sedentary, as people exercised less.