Genomic structural alterations that vary within species, known as large copy number variants, represent an unanticipated and abundant source of genetic diversity that associates with variation in gene expression and susceptibility to disease. Even short insertions and deletions (indels) can exert important effects on genomes by locally increasing the mutation rate, with multiple mechanisms proposed to account for this pattern. To better understand how indels promote genome evolution, we demonstrate that the single nucleotide mutation rate is elevated in the vicinity of indels, with a resolution of tens of base pairs, for the two closely related nematode species Caenorhabditis remanei and C. sp. 23. In addition to indels being clustered with single nucleotide polymorphisms and fixed differences, we also show that transversion mutations are enriched in sequences that flank indels and that many indels associate with sequence repeats. These observations are compatible with a model that reconciles previously proposed mechanisms of indel-associated mutagenesis, implicating repeat sequences as a common driver of indel errors, which then recruit error-prone polymerases during DNA repair, resulting in a locally elevated single nucleotide mutation rate. The striking influence of indel variants on the molecular evolution of flanking sequences strengthens the emerging general view that mutations can induce further mutations.