The research, carried out at the Foundation for Nutrition Research in Helsinki, quizzed 827 volunteers aged 16 to 21 for symptoms of gastrointestinal disorders.
Further examination by duodenal biopsy was done for 49 people who reported problems and 29 who did not.
At the start, a quarter of all study participants claimed that cow's milk caused them problems, and a 13 per cent said they did not drink milk at all.
The results of the biopsies showed that those with gastrointestinal problems did have higher intraepithelial cell counts and other markers for food-related allergy than the control group. However, these markers were not those associated with cow's milk.
Dr. Laura Paajanen, lead researcher on the study, said, "the finding of immunological activity implied the existence of a food-related gastrointestinal syndrome but not one induced by cow's milk."
While allergic reactions to cow's milk are known to occur in school-age children, the problem has not previously been studied for young adults.
In an additional blind experiment people with gastrointestinal problems were divided into two groups. One group was given cow's milk, while the other was given a placebo drink containing soy.
Only 2 of 23 participants in the first group showed symptoms associated with a milk allergy.
Allergy to cow's milk is estimated to affect between 0.5 and 4 per cent of all infants, but 90 per cent of those have usually grown out of the allergy by the age of three.
The results are published in the American Journal of Clinical Nutrition (Vol. 82, No. 6, pp. 1327-1335).
A 250 ml serving of semi-skimmed milk contains 40 per cent of the RDA for calcium and 50 per cent of the RDA for vitamin D.
People who avoid milk because they wrongly believe they are lactose intolerant are in danger of missing out on important nutrients.
Milk contains 15 vitamins and minerals, including significant amounts of calcium, vitamin D, riboflavin and vitamin B12.