The finding comes from a study of 460 children living in Minorca, a Spanish island in the Mediterranean.
The kids, who were nearly 7 years old, didn't go on a special diet for the researchers, who included Leda Chatzi, MD, PhD, of the University of Crete's social medicine department.
Most of the kids didn't wheeze or have allergies, and their typical diet was pretty healthy, according to the moms' surveys.
Kids who ate the most tomatoes, eggplants, cucumbers, green beans, and zucchini -- more than 40 grams per day -- were at least 62% less likely to wheeze, compared with kids who skimped on those vegetables.
Chatzi and colleagues call those veggies "fruity vegetables" to distinguish them from root vegetables or leafy vegetables.
Only fruity vegetables -- not fruits, root vegetables, leafy veggies, or other foods -- were linked to lower likelihood of wheeze.
The study also shows that kids who ate more than 60 grams of fish per day were 57% less likely to test positive for allergies as those who ate the least amount of fish (up to about 39 grams per day of fish).
The findings didn't change when the researchers considered factors including whether the kids had been breastfed as babies, or whether their moms smoked, or where their parents ranked in terms of education or social class.
Still, the study didn't directly test fish and vegetables to prevent asthma and allergies. The findings appear in the journal Pediatric Allergy and Immunology.