Memory consolidation can benefit from post-learning sleep, eventually leading to long-term microstructural brain modifications to accommodate new memory representations. Non-invasive diffusion-weighted magnetic resonance imaging (DWI) allows the observation of (micro)structural brain remodeling after time-limited motor learning. Here, we combine conventional diffusion tensor imaging (DTI) and neurite orientation dispersion and density imaging (NODDI) that allows modeling dendritic and axonal complexity in gray matter to investigate with improved specificity the microstructural brain mechanisms underlying time- and sleep-dependent motor memory consolidation dynamics. Sixty-one young healthy adults underwent four DWI sessions, two sequential motor trainings, and a night of total sleep deprivation or regular sleep distributed over five days. We observed rapid-motor-learning-related remodeling in occipitoparietal, temporal, and motor-related subcortical regions, reflecting temporary dynamics in learning-related neuronal brain plasticity processes. Sleep-related consolidation seems not to exert a detectable impact on diffusion parameters, at least on the timescale of a few days.