Thousands of children have been spared serious illness and hospital treatment since the smoking ban was introduced in England in 2007, research suggests.
The study, in the European Respiratory Journal, looked at 1.6 million hospital admissions of under-14s from 2001-12.
The law against smoking in indoor public places saw 11,000 fewer children being admitted to hospital with lung infections every year, it found.
Researchers said it showed anti-smoking legislation was improving child health.
The University of Edinburgh study compared the figures for hospital admissions after the ban with mathematical predictions of the number of admissions that would have occurred without the smoking ban.
It estimated that hospital admissions for children with respiratory infections fell by 3.5% immediately after the ban was introduced.
While the biggest effect was seen in the number of children suffering chest infections - which dropped by almost 14% - the number of admissions attributable to nose, throat and sinus infections also went down.
But these effects were more gradual, the study said.
There is a well-established link between second-hand smoke exposure and bronchitis, bronchiolitis, middle ear infections and respiratory tract infections.
Dr Jasper Been, of the University of Edinburgh and Maastricht University, said: "This study is further demonstration of the considerable potential of anti-smoking laws to improve child health.
"Although our results cannot definitively establish a cause and effect, the rigorous analysis clearly shows that the introduction of smoke-free legislation was associated with significant reductions in hospital admissions among children."
Data suggested the ban on smoking in public places had also led to a rise in the number of smoke-free homes, reducing second-hand smoke exposure among children, the study said.
The ban is estimated to have reduced adults smoking in the home from 65% to 55%.
Professor Aziz Sheikh, co-director of the University of Edinburgh's Centre for Population Health Sciences, said: "The many countries that are yet to enforce smoke-free legislation should consider the substantial number of hospital admissions from respiratory infections that occur each year that they delay."
Less than one sixth of the world's population is currently protected by anti-smoking laws.
It is estimated that about 40% of children around the world are regularly exposed to second-hand smoke.
Hazel Cheeseman, director of policy at health charity Ash (Action on Smoking and Health), said: "Back in 2007, the opponents of smoke-free legislation claimed that it would lead to more people smoking at home, placing their children at greater risk.
"This research supports evidence from elsewhere that this fear has not been realised.
"Without the ban on smoking in public places the NHS would be seeing more sick children at a significant cost to the public purse."