Researchers from Finland found that giving the bacteria, first to the mother prior to birth, then to the baby postnatally, halved the rate of eczema in these vulnerable children.
This suggests that the regimen may have a beneficial effect against other allergy-related illnesses, such as asthma and hayfever.
Allergy is a growing disease in modern times, affecting an estimated half the population in more-developed countries.
The study, at the University of Turku, split a group of 132 pregnant women into two groups - with half given the supplement, containing bacteria Lactobacillus GG.
Family history
All the study participants had a family history of allergic disease such as eczema or asthma - making their children at higher risk of developing such illnesses themselves.
Tablets were taken by the women two weeks before delivery, and in the following six months
The babies were also tested for the presence of antibodies in their blood which might suggest a developing allergy to common triggers like house dust mite, milk, egg and cat.
Although these tests showed little difference between the group taking the probiotic, and the group taking the ingredient-free placebo, far fewer children receiving the bacteria developed eczema.
The study's author, Marko Kalliomaki, said: "Our results suggest that gut microflora have unique, yet largely unexplored, endogenous immunomodulatory properties.
"These properties might by indispensable in the fight against the increasing frequency of atopic, and possibly other, immunological disease."
The figures were described as "remarkable" by an expert in allergic disease from London's Royal Free Hospital.
Dr Simon Murch said: "If confirmed in other studies, and applicable to other allergic diseases, probiotics would represent an important therapeutic advance."
While the association between so-called "friendly bacteria", and redued allergy, has been noted before, no-one is sure why they should have such an effect.