The degree to which glaucoma has effects in the brain beyond the eye and the visual pathways is unclear. To clarify this, we investigated white matter microstructure (WMM) in 37 tracts of patients with glaucoma, monocular blindness, and controls. We used brainlife.io for reproducibility. White matter tracts were subdivided into seven categories ranging from those primarily involved in vision (the visual white matter) to those primarily involved in cognition and motor control. In the vision tracts, WMM was decreased as measured by fractional anisotropy in both glaucoma and monocular blind subjects compared to controls, suggesting neurodegeneration due to reduced sensory inputs. A test-retest approach was used to validate these results. The pattern of results was different in monocular blind subjects, where WMM properties increased outside the visual white matter as compared to controls. This pattern of results suggests that whereas in the monocular blind loss of visual input might promote white matter reorganization outside of the early visual system, such reorganization might be reduced or absent in glaucoma. The results provide indirect evidence that in glaucoma unknown factors might limit the reorganization as seen in other patient groups following visual loss.