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.
More top news
Defence Secretary Michael Fallon has said Boris Johnson's comments about Saudi Arabia "playing proxy wars" were taken out of context.
Home Office files on the Battle of Orgreave are due to be released next year among a host of records relating to the 1984 miners' strike.
Tara Christmas's kitten Elsa was put on a drip when she collapsed last Christmas after eating the leaves of the festive plant.