Simon Nicholas Williams, from Cambridge University's Institute of Public Health, said that three-quarters of adult mental disorders were "extensions of juvenile disorders".
"If left untreated, these can lead to more serious social and economic problems in adolescence and adulthood, related to crime, unemployment, and suicide, for example," he wrote.
He said early intervention and prevention of mental health problems should be aimed at young people.
"Introducing mental health screening in schools could enable early diagnosis and treatment of childhood mental health problems and therefore reduce many of the costs associated with adolescent and adult mental health problems," he wrote.
He said mental health problems cost the UK an estimated £105bn a year.
"Physical health checks have been done in schools for more than a century, so why not mental health checks?", he added.
Russell Hobby, leader of the National Association of Head Teachers (NAHT), said any such scheme would have to be carefully handled.
"I think we should be checking children for much more than whether they have mastered phonics," he said.
"The evidence suggests that the earlier we start checking people, the better. But schools themselves are not qualified to do this and health professionals would have to be involved."
Mr Hobby added: "We would have to be quite careful about any labels and stigma attached to this. It would have to be done in a sensitive fashion."