It found admissions dropped by about 25% in four years following the 2014 Take it Right Outside campaign.
The study looked at all hospital admissions in Scotland between 2000-2018 for those aged 16 and under.
It was conducted by the Universities of Aberdeen, Stirling and Glasgow.
The study noted that the same reduction was not observed in children aged over five over the same period.
It said this could possibly be because these children spend less time in the home and are in less close contact with a parent who smokes.
Prof Steve Turner, a consultant paediatrician at Aberdeen University said: "This study shows there was a fall in asthma admissions among children aged under five relative to the underlying trend after Take it Right Outside was launched.
"Whilst we cannot say conclusively that one is a direct result of the other, the figures are encouraging and suggests that public health mass media campaigns that compliment broader changes in legislation can make a difference."