The results come from data compiled in the BAMSE study, which includes 4,000 Stockholm-area children and is one of the world's largest allergy studies.
The study represents the first time that researchers have been able to differentiate between the effects passive smoking which occurs during pregnancy and outside the womb.
Children whose parents smoked during pregnancy were four times more likely to develop asthma before their fourth birthday.
Children who were exposed to smoke after birth were more often affected by allergies than children from smoke-free homes.
The strongest link was found between passive smoking and cat allergies.
"This is particularly worrying as cat allergens are almost everywhere and are hard to avoid," said the study's author Dr. Eva Lannerö, in a statement.
"We can't say how many, but some of these children will definitely develop chronic asthma."