Background: According to the cognitive reserve (CR) theory, enriching experiences protect against cognitive decline. Objectives: To investigate the dynamic interaction between CR and global/regional measures of brain white matter (WM) and gray matter (GM) damage and their effect on cognitive performance in multiple sclerosis (MS). Methods: Baseline and 2 -year three-dimensional (3D) T1-weighted scans were obtained from 54 MS patients and 20 healthy controls. Patients’ cognitive functions were tested and a cognitive reserve index (CRI) was calculated. Baseline regional atrophy and longitudinal volume changes were investigated using voxel-wise methods. Structural damage and CRI effects on cognitive performance were explored with linear models. Results: At baseline, MS patients showed atrophy of the deep GM nuclei, GM/WM frontal–temporal–parietal–occipital regions, and left cerebellum. Controlling for atrophy, higher CRI explained significant portions of variance in verbal memory and verbal fluency (∆ R² = 0.07–0.16; p < 0.03). The interaction between thalamic volume and CRI was significant (∆ R² = 0.05; p = 0.03). Longitudinal changes in memory and attention performance were associated with local/global variations of GM/WM and T2 lesions. CRI had no effect on longitudinal cognitive changes. Conclusion: In MS, CR may have a protective role in preserving cognitive functions, moderating the effect of structural damage on cognitive performance. This protective role may diminish with disease progression.