While studies suggest that socioeconomic position (SEP) influences bone health and risk of osteoporotic fracture in postmenopausal women, few studies have simultaneously examined gender and menopause differences as they relate to SEP and bone health. Here, we investigated the relationship between SEP and bone mineral density (BMD) among Korean men, premenopausal women, and postmenopausal women using the BMD data set (n = 9,995) of the Korean National Health and Nutrition Examination Survey IV. The relationship between SEP and BMD was estimated using analysis of covariance (ANCOVA); adjustments were made for age and body mass index (BMI) in the multivariate models. The relationship between SEP and osteoporosis prevalence was estimated using logistic regression. Relative index of inequality (RII) in osteoporosis was estimated using log-binomial regression. ANCOVA (adjusted for age and for age plus BMI) showed a significant positive association between SEP and BMD among men and postmenopausal women. Logistic regression showed a significant negative association between SEP and osteoporosis prevalence among men and postmenopausal women but not in premenopausal women. The RII, estimated by log-binomial regression, showed the impact of SEP on osteoporosis to be significant in men and postmenopausal women (p < 0.05) but not in premenopausal women. Overall, low SEP was associated with both low BMD and high risk of osteoporosis among men and postmenopausal women. Efforts to reduce the economic burden of morbidity and mortality from osteoporosis should target men and postmenopausal women with low SEP.