The University of Auckland's Professor Innes Asher, who led the study, said parents should sit up and take notice of the results.
"These results are quite concerning, because fast food outlets are on the rise," Prof Asher said.
"The bottom line is that people should be careful about the amount of fast food they eat."
Though the exact reason why consumption of fast food is linked to these conditions is unknown, Prof Asher cites factors such as high levels of trans- and saturated- fatty acids as possible contenders.
These fats are known to affect immunity, which could in turn lead to allergy-related conditions.
Eating fresh fruit provides protection against these conditions because they contain beneficial antioxidants, she said.
The study indicates an association between the factors, rather than establishing a causal link.
The research team is currently looking for funding for a future study, which would establish whether this link is present.
If causality is established, then "the findings have major public health significance owing to the rising consumption of fast foods globally," Prof Asher said.