International scientists conducting the new study looked at data on more than 2.5 million births and almost 250,000 hospital visits for asthma attacks.
Dr Jasper Been, from the University of Edinburgh, said:
Our research shows that smoking bans are an effective way to protect the health of our children.
These findings should help to accelerate the introduction of anti-smoking legislation in areas not currently protected.
Professor Aziz Sheikh, co-director of the university's Centre for Population Health Sciences, said:
This research has demonstrated the very considerable potential that smoke-free legislation offers to reduce pre-term births and childhood asthma attacks.
The many countries that are yet to enforce smoke-free legislation should in the light of these findings reconsider their positions on this important health policy question.
The findings are reported in the latest edition of The Lancet medical journal.