Glaucoma is the world's leading cause of irreversible blindness, and falls are a major public health concern in glaucoma patients. Although recent evidence suggests the involvements of the brain toward advanced glaucoma stages, the early brain changes and their clinical and behavioral consequences remain poorly described. This study aims to determine how glaucoma may impair the brain structurally and functionally within and beyond the visual pathway in the early stages, and whether these changes can explain visuomotor impairments in glaucoma. Using multi-parametric magnetic resonance imaging, glaucoma patients presented compromised white matter integrity along the central visual pathway and around the supramarginal gyrus, as well as reduced functional connectivity between the supramarginal gyrus and the visual occipital and superior sensorimotor areas when compared to healthy controls. Furthermore, decreased functional connectivity between the supramarginal gyrus and the visual brain network may negatively impact postural control measured with dynamic posturography in glaucoma patients. Taken together, this study demonstrates that widespread structural and functional brain reorganization is taking place in areas associated with visuomotor coordination in early glaucoma. These results implicate an important central mechanism by which glaucoma patients may be susceptible to visual impairments and increased risk of falls.