Chromosomal inversions are an important form of structural variation that can affect recombination, chromosome structure and fitness. However, because inversions can be challenging to detect, the prevalence and hence the significance of inversions segregating within species remains largely unknown, especially in natural populations of mammals. Here, by combining population-genomic and long-read sequencing analyses in a single, widespread species of deer mouse (Peromyscus maniculatus), we identified 21 polymorphic inversions that are large (1.5–43.8 Mb) and cause near-complete suppression of recombination when heterozygous (0–0.03 cM Mb−1). We found that inversion breakpoints frequently occur in centromeric and telomeric regions and are often flanked by long inverted repeats (0.5–50 kb), suggesting that they probably arose via ectopic recombination. By genotyping inversions in populations across the species’ range, we found that the inversions are often widespread and do not harbour deleterious mutational loads, and many are likely to be maintained as polymorphisms by divergent selection. Comparisons of forest and prairie ecotypes of deer mice revealed 13 inversions that contribute to differentiation between populations, of which five exhibit significant associations with traits implicated in local adaptation. Taken together, these results show that inversion polymorphisms have a significant impact on recombination, genome structure and genetic diversity in deer mice and likely facilitate local adaptation across the widespread range of this species.