Despite the fact that complete visual deprivation leads to volumetric reductions in brain structures associated with spatial learning, blind individuals are still able to navigate. The neural structures involved in this function are not fully understood. Our study aims to correlate the performance of congenitally blind individuals (CB) and blindfolded sighted controls (SC) in a life-size obstacle-course using a visual-to-tactile sensory substitution device, with the size of brain structures (voxel based morphometry-VBM-) measured through structural magnetic resonance Imaging (MRI). VBM was used to extract grey matter volumes within several a-priori defined brain regions in all participants. Principal component analysis was utilized to group brain regions in factors and orthogonalize brain volumes. Regression analyses were then performed to link learning abilities to these factors. We found that (1) both CB and SC were able to learn to detect and avoid obstacles; (2) their learning rates for obstacle detection and avoidance correlated significantly with the volume of brain structures known to be involved in spatial skills. There is a similar relation between regions of the dorsal stream network and avoidance for both SC and CB whereas for detection, SC rely more on medial temporal lobe structures and CB on sensorimotor areas.