In a project funded by the Action Research charity, Dr Nicola Keay examined 57 women over the age of 20 who had not yet reached the menopause, and measured the mineral bone density of their spine and pelvis.
She found that in those whose periods had stopped the spine measurements were significantly below those of other women.
But in dancers with normal periods the bone density in the hips was significantly higher than that of the general population - an apparent benefit of training.
Dr Keay, of St Thomas' Hospital, London, says: "I am not saying that these women should not carry on dancing.
"I hope our study will highlight ways of reducing the risk of stress fractures due to low bone density."
Osteoporosis affects more than three million people in Britain. It generally affects women after the menopause and can lead to painful fractures of the spine, hips and wrists.