The findings are based on a representative population sample of more than 12000 adults in the USA, taking part in the 2002 National Health Interview Survey.
Participants were asked if they had ever been diagnosed with a disorder of the thyroid gland and/or the eye disease glaucoma.
The thyroid makes hormones that are essential for the function of every cell in the body. These hormones help regulate growth and the rate of chemical reactions.
Glaucoma is characterised by progressive damage to the optic nerve. If not treated, it leads to loss of central (fine detailed) vision and blindness. It is the leading cause of irreversible blindness worldwide.
The prevalence of glaucoma was just over 4.5% among those surveyed, and just under 12% of respondents said they had had a thyroid disorder.
The proportion of those with glaucoma who said they had had a thyroid problem at some point in their lives was 6.5%.
This compares with a rate of 4.4% among those who said they had not been diagnosed with a thyroid disorder.
After taking account of risk factors, including gender, race, and smoking habit, the association between glaucoma and thyroid problems remained significant.
People with glaucoma were 38% more likely to have had a thyroid disorder diagnosed at some point in their life.
A biological link between the two conditions is plausible, explain the authors.
An underactive thyroid (hypothyroidism) can promote chemical deposits in the mesh of vessels serving the eye, which can spark an increase in pressure within the eyeball. This is a cardinal feature of glaucoma.
Given that the prevalence of both conditions is relatively high, further research will be needed to confirm the findings, caution the authors.
This includes whether prompt treatment of thyroid problems could stave off the risk of subsequent glaucoma, they say.