All the patients experienced reduced pain, the scientists said.
They also found that the blood glucose levels of all the patients were much higher than the levels in normal people.
Neurology professor Dr Miguel Pappolla said previous studies had overlooked the connection between fibromyalgia and A1c levels.
He added: “The main reason for this oversight is that about half of fibromyalgia patients have A1c (blood glucose) values currently considered within the normal range.
“However, this is the first study to analyse these levels normalised for the person’s age, as optimal A1c levels do vary throughout life.
“Adjustment for the patients’ age was critical in highlighting the differences between patients and control subjects.”
Pre-diabetes sufferers who had slightly higher A1c values had a higher risk of developing headaches, a symptom of fibromyalgia and other chronic pain disorders, he said.
Treatment for fibromyalgia includes medication such as antidepressants and painkillers, talking therapies, exercise and relaxation techniques.
The cause is thought to be related to abnormal levels of certain chemicals in the brain and changes in the way the central nervous system processes pain messages carried around the body.
The NHS adds: “It’s also suggested that some people are more likely to develop fibromyalgia because of genes inherited from their parents.”
In many cases it appears to be triggered by a physically emotional or stressful event such as an injury, childbirth, an operation, a break-up or the death of a loved one.
Fibromyalgia Action UK says of the condition: “The pain tends to be felt as diffuse aching or burning, often described as head to toe.
“It may be worse at some times than at others.
“It may also change location, usually becoming more severe in parts of the body that are used the most.
“The fatigue ranges from feeling tired, to the exhaustion of a flu-like illness.
“It may come and go and people can suddenly feel drained of all energy – as if someone just ‘pulled the plug’.”