But only one in four women who have trouble sleeping tell their doctor, according to the poll, meaning the problem is likely to be much greater that is thought.
Experts warn that not getting enough sleep can be a warning sign of an underlying severe medical condition.
The Harvard team divided those they studied into groups, depending on how many different sleep disorders they reported.
The four problems they recorded were sleeping difficulty, frequent snoring, sleeping for less than six hours a night, and sleep apnoea, in which sufferers stop breathing repeatedly while they sleep.
Those who reported one sleep disorder were 47 per cent more likely to develop type 2 diabetes, those who reported having two conditions had around twice the risk, while for three conditions it was approximately three times the risk, and for all four it was four times the risk.
Writing in the journal Diabetologia, the authors said: "Sleeping difficulty was significantly associated with type 2 diabetes.
"Our findings highlight the importance of good sleeping patterns and having enough sleep for preventing type 2 diabetes."
- Daily Mail