Stillbirths have dropped by almost eight per cent in England since the smoking ban was introduced, research shows.
The number of babies dying shortly after birth has also dropped by almost eight per cent, the study estimates.
The findings add to growing evidence that anti-smoking laws have had significant benefits for infant and child health.
Researchers led by the University of Edinburgh looked at information on more than ten million births in England between 1995 and 2011.
Their findings suggest that almost 1500 stillbirths and newborn deaths were averted in the first four years after the law to prohibit smoking in public places was introduced.
The team also assessed the impact of the smoking ban on the number of babies born with a low birth weight, which is linked to health complications in later life including heart disease and diabetes.
More than five thousand fewer babies were born with a low birth weight of less than two and a half kilograms the researchers estimate.
Smoking and smoke-exposure during pregnancy are known to have long-term adverse effects on the health of unborn children, including increased risk of diabetes and heart disease.
The researchers have previously shown that rates of premature births have dropped significantly in countries where smoke-free legislation has been introduced. The number of children being admitted to hospital for asthma attacks and severe respiratory infections has also fallen since the bans.
This is the first study to show that smoke-free legislation is helping to reduce the risk of babies dying before or shortly after birth. It was conducted by researchers at the Universities of Edinburgh and Glasgow, Imperial College London, the Erasmus University Medical Centre and Maastricht University in the Netherlands, Harvard Medical School and Brigham and Women's Hospital in the US.
The study is published in the journal Scientific Reports. It was funded by the Thrasher Research Fund and the International Pediatric Research Foundation.
Dr Jasper Been, Honorary Research Fellow at the University of Edinburgh and Paediatrician at the Erasmus University Medical Centre in Rotterdam, said: "Currently, only around 18 per cent of the world's population is protected by comprehensive smoke-free laws. Accelerated action to implement smoking bans in the many countries yet to do so is likely to save considerable numbers of young lives and bring a healthier future for our unborn children."
Professor Aziz Sheikh, Co-director of the University of Edinburgh's Centre for Medical Informatics, said: "This study is further evidence of the potential power of smoke-free legislation to protect present and future generations from the devastating health consequences of smoking and second hand exposure to tobacco smoke."