Scientists who led the investigation said the results were unprecedented and may explain the continuing rise in the number of people with myopia, a condition that can lead to serious sight problems in later life.
The study also found that children who slept with higher power bulbs - such as an overhead light - are up to five times more likely to develop myopia, indicating that the effect becomes worse with brighter night-time light.
"This is the first time that this kind of question has been asked in children," said Richard Stone, professor of ophthalmology at Pennsylvania University medical centre in Philadelphia. "The dose effect, with a stronger light leading to a stronger effect, makes it more plausible that there is something going on," he said.
"This is really new and there's no precedent in the medical literature. It appears that a daily period of darkness is needed for the post-natal development of the eyes."
A survey of the parents of 479 children aged between two and 16 whose eyesight was measured by hospital doctors revealed that night-time light levels were only important in the first two years of life, according to a scientific paper published in the journal Nature.
About 10 per cent of the children in the study who had slept in the dark before the age of two were shortsighted, compared with 34 per cent who had slept with a low-power night-light and more than than 50 per cent who had slept with a room light on. Professor Stone said the eye undergoes its most rapid growth during the first two years of life and it is possible that this is stimulated by night-time light levels. Other scientists have shown that young chicks reared in henhouses with 24-hour light develop larger eyes.
Bigger eyes are more prone to be myopic because they have longer distances between lens and the back of the eye, causing light to be focused on a point just short of the retina. Graham Quinn, a paediatric ophthalmologist at the Children's Hospital in Philadelphia, said light at night can penetrate a closed eyelid and its association with myopia may have important repercussions.
"Especially in the more severe degrees, myopia itself is a leading risk factor for acquired blindness, putting people at risk for retinal detachment, retinal degeneration and glaucoma," he said.
Professor Stone said the study has not proved a cause-and-effect relationship, but the association is too strong to ignore. "My recommendation is for parents to take reasonable measures. When children under two are asleep at night, they should just turn out the light in the room," he said.