Headache is among the most frequently reported symptoms after resolution of COVID-19. We assessed structural brain changes using T1- and diffusion-weighted MRI processed data from 167 subjects: 40 patients who recovered from COVID-19 but suffered from persistent headache without prior history of headache (COV), 41 healthy controls, 43 patients with episodic migraine and 43 patients with chronic migraine. To evaluate gray matter and white matter changes, morphometry parameters and diffusion tensor imaging-based measures were employed, respectively. COV patients showed significant lower cortical gray matter volume and cortical thickness than healthy subjects (p < 0.05, false discovery rate corrected) in the inferior frontal and the fusiform cortex. Lower fractional anisotropy and higher radial diffusivity (p < 0.05, family-wise error corrected) were observed in COV patients compared to controls, mainly in the corpus callosum and left hemisphere. COV patients showed higher cortical volume and thickness than migraine patients in the cingulate and frontal gyri, paracentral lobule and superior temporal sulcus, lower volume in subcortical regions and lower curvature in the precuneus and cuneus. Lower diffusion metric values in COV patients compared to migraine were identified prominently in the right hemisphere. COV patients present diverse changes in the white matter and gray matter structure. White matter changes seem to be associated with impairment of fiber bundles. Besides, the gray matter changes and other white matter modifications such as axonal integrity loss seemed subtle and less pronounced than those detected in migraine, showing that persistent headache after COVID-19 resolution could be an intermediate state between normality and migraine.