While nutritionists warn that the high number of malnourished children still to be found in such countries should remain a priority, they believe that any obesity increase is a cause for concern.
A new study, carried out by the World Health Organisation, found that on average, the global prevalence of overweight pre-school children was 3.3%.
But some developing countries had much higher rates.
In countries such as Egypt, Chile, Armenia and Algeria, for example, the rate was well over 5%. In Uzbekistan, it was approaching 15%.
The WHO investigation, published in the American Journal of Epidemiology, confirmed that in many countries, the trend was towards more overweight children.
Health problems 'inherited'
Dr Mercedes de Onis, the lead author, told BBC News Online: "The problem is, when you introduce the diets of developed countries, you inherit the health problems of developed countries.
"In Western countries, child obesity is a major epidemic, and now is the time to do something about it in the developing world to stop it getting that bad."
Dr de Onis said she was hopeful that education programmes aimed at children could encourage healthier eating.
Another factor in keeping children slimmer and healthier was breastfeeding, she said.
Mothers who breastfeed are more likely to have children who are better able to regulate their weight.
However, many mothers in developing countries have been persuaded to move to formula milk soon after birth, which means that subsequent attempts to breastfeed will fail.
Health perils highlighted
However, Dr de Onis stressed that the health perils to malnourished and severely underweight children greatly outweighed those caused by overeating or eating unhealthy foods.
In many African countries, along with India and Bangladesh, the proportion of under-fives who are underweight approached or even exceeded 15%.
When it comes to overweight children, even the worst-affected countries have some way to travel before they reach the levels of Europe and particularly the US.
In the latter, almost one-in-three children are overweight even before they reach school age.