Over the last 15 years, research on canid cognition has revealed that domestic dogs possess a surprising array of complex sociocognitive skills pointing to the possibility that the domestication process might have uniquely altered their brains; however, we know very little about how evolutionary processes (natural or artificial) might have modified underlying neural structure to support species-specific behaviors. Evaluating the degree of cortical folding (i.e., gyrification) within canids may prove useful, as this parameter is linked to functional variation of the cerebral cortex. Using quantitative magnetic resonance imaging to investigate the impact of domestication on the canine cortical surface, we compared the gyrification index (GI) in 19 carnivore species, including six wild canid and 13 domestic dog individuals. We also explored correlations between global and local GI with brain mass, cortical thickness, white and gray matter volume and surface area. Our results indicated that GI values for domestic dogs are largely consistent with what would be expected for a canid of their given brain mass, although more variable than that observed in wild canids. We also found that GI in canids is positively correlated with cortical surface area, cortical thickness and total cortical gray matter volumes. While we found no evidence of global differences in GI between domestic and wild canids, certain regional differences in gyrification were observed.