The findings were revealed in a study of nearly 4300 secondary pupils by Strathclyde University.
Researchers found the vast majority had not been bullied at all.
However, those who had – and felt worried about it – were found to be nearly 20 times more likely to suffer from lack of sleep.
The findings will be presented today at a conference of the British Psychological Society at Strathclyde University.
Dr Simon Hunter, a senior lecturer in psychology at the university, who led the research, called for more help for bullied pupils to cope with the symptoms.
"Lack of sleep can bring other health problems along with it and, if young people can be helped to develop strategies to help them deal with bullying worries, it could enable them to sleep better," he said.
Brian Donnelly, director of Scottish anti-bullying charity Respectme, said sleeplessness was just one symptom of bullying.
"Anxiety is the key response and that can manifest itself in a range of ways from withdrawal to aggression," he said. "Some impacts will not manifest themselves for years."
The conference will also hear research from a study by Cambridge University.
Starting in 1961, the study assessed 411 eight-year-old boys from London and followed them until age 48.
The results showed 18% of those identified as bullies at the age 14 had been subsequently convicted for a violent offence, while 39% had been convicted of a criminal offence. However, bullies with higher IQs were less likely to offend after leaving school.