Background. Improvement of postural control in persons with multiple sclerosis (PwMS) is an important target for neurorehabilitation. Although PwMS are able to improve postural performance with training, the neural underpinnings of these improvements are poorly understood. Objective. To understand the neural underpinnings of postural motor learning in PwMS. Methods. Supraspinal white matter structural connectivity in PwMS was correlated with improvements in postural performance (balancing on an oscillating surface over 25 trials) and retention of improvements (24 hours later). Results. Improvement in postural performance was directly correlated to microstructural integrity of white matter tracts, measured as radial diffusivity, in the corpus callosum, posterior parieto-sensorimotor fibers and the brainstem in PwMS. Within the corpus callosum, the genu and midbody (fibers connecting the prefrontal and primary motor cortices, respectively) were most strongly correlated to improvements in postural control. Twenty-four-hour retention was not correlated to radial diffusivity. Conclusion. PwMS who exhibited poorer white matter tract integrity connecting the cortical hemispheres via the corpus callosum showed the most difficulty learning to control balance on an unstable surface. Prediction of improvements in postural control through training (ie, motor learning) via structural imaging of the brain may allow for identification of individuals who are particularly well suited for postural rehabilitation interventions.