Scientists in Denmark believe the link may be due to stress caused by the pain of the procedure.
The study of more than 340,000 boys found that circumcision raised the overall chances of an autism spectrum disorder (ASD) before the age of 10 by 46%.
But if circumcision took place before the age of five it doubled the risk.
Circumcision also appeared to increase the likelihood of boys from non-Muslim families developing hyperactivity disorder.
Professor Morten Frisch, of the Statens Serum Institut, Copenhagen, who led the research, said: "Our investigation was prompted by the combination of recent animal findings linking a single painful injury to lifelong deficits in stress response and a study showing a strong, positive correlation between a country's neonatal male circumcision rate and its prevalence of ASD in boys."
While it is considered unacceptable today to circumcise boys without proper pain relief, it is not possible to make the procedure completely pain-free.
The pain of circumcision is likely to be more severe in very young babies both during and after the operation, according to the scientists.
Painful experiences in newborns have been shown in both animal and human studies to be associated with long-term alterations in pain perception, a characteristic often seen in autistic children.
Prof Frisch added: "Possible mechanisms linking early life pain and stress to an increased risk of neurodevelopmental, behavioural or psychological problems in later life remain incompletely conceptualised.
"Given the widespread practice of non-therapeutic circumcision in infancy and childhood around the world, our findings should prompt other researchers to examine the possibility that circumcision trauma in infancy or early childhood might carry an increased risk of serious neurodevelopmental and psychological consequences."
The findings are reported in the Journal of the Royal Society of Medicine.
Professor David Katz, from University College London, who chairs Milah UK, a body that speaks for the Jewish community on issues related to circumcision, said: "This report is far from convincing: correlation does not equal causation.
"There is a long history of attempts to link autistic spectrum disorders to unrelated practices, such as the measles/mumps/rubella association, which proved to be fraudulent.
"There is general agreement that in people suffering from an ASD there are abnormalities that can be identified in brain structure and/or function.
"There is a strong genetic component, which may be a factor within the faith communities studied here, and which does not appear to have been explored amongst them.
"Some contemporary research does indicate that factors besides the genetic component are contributing to the increasing occurrence of ASD - for example, a variety of environmental toxins have been invoked to explain why these conditions are more prevalent today than they may have been in the past - but again proof of causation is lacking, and these factors are only likely to be relevant in those who are already vulnerable to them."
Applied statistician Professor Kevin McConway, from the Open University, said: "This study raises an interesting question, but one that cannot be fully answered with these data.
"The study is observational, and in such studies it's always tricky to tell what causes what. The observed increase in risk of autism spectrum disorder in circumcised boys might be due to the circumcision, or it might not.
"Religions that prescribe circumcision prescribe other things too, such as diet or clothing. Perhaps differences in diet or clothing lead to the increased ASD risk, rather than the circumcision. Cultural and family differences may be crucial."