Summary Older women with low bone mass are at higher risk of fracture and there is limited data on what is associated with risk of falls. We found explosive jumping to relate most strongly to postural control. It may be beneficial to include power or speed training into falls prevention programs. Introduction Post-menopausal women with low bone mass are at higher risk of bone fractures subsequent to falls. Understanding the correlates of postural control in this collective informs intervention design for falls prevention. Methods We examined postural control in single-leg stance on stable and unstable surfaces in 63 community-dwelling post-menopausal women with osteopenia or osteoporosis but without diagnosed neuromuscular, vestibular or arthritic diseases. Postural measures were compared to countermovement jump performance (height, force and power), leg-press strength (10 repetition maximum), calf muscle area and density (via peripheral quantitative computed tomography), body mass, height and age. Results On step-wise regression, peak countermovement jump power and jump height ( p  ≤ 0.014), but not jump force, leg-press strength or calf muscle size, were related to postural control in single-leg stance on, respectively, an unstable surface (eyes open) and standing on a stable surface (eyes open). None of the parameters measured were significantly related to the postural control parameters in single-leg stance on a stable surface with eyes closed. With testing on the stable surface, body mass was associated with slow mean centre of pressure movement speed ( p  ≤ 0.030). Conclusions Our findings show that, in post-menopausal women with low bone mass, neuromuscular power is a more important determinant of postural control than muscle strength or size. Our findings provide evidence to support the integration of power or speed training into falls prevention and balance training programs in post-menopausal women with osteopenia and osteoporosis.