Objective Obstructive sleep apnea (OSA) is accompanied by brain changes in areas that regulate autonomic, cognitive, and mood functions, which were initially examined by Gaussian-based diffusion tensor imaging measures, but can be better assessed with non-Gaussian measures. We aimed to evaluate axonal and myelin changes in OSA using axial (AK) and radial kurtosis (RK) measures. Materials and Methods We acquired diffusion kurtosis imaging data from 22 OSA and 26 controls; AK and RK maps were calculated, normalized, smoothed, and compared between groups using analysis of covariance. Results Increased AK, indicating axonal changes, emerged in the insula, hippocampus, amygdala, dorsolateral pons, and cerebellar peduncles and showed more axonal injury over previously identified damage. Higher RK, showing myelin changes, appeared in the hippocampus, amygdala, temporal and frontal lobes, insula, midline pons, and cerebellar peduncles and showed more widespread myelin damage over previously identified injury. Conclusions Axial kurtosis and RK measures showed widespread changes over Gaussian-based techniques, suggesting a more sensitive nature of kurtoses to injury.