Short tandem repeats (STRs) are a class of rapidly mutating genetic elements typically characterized by repeated units of 1–6 bp. We leveraged whole-genome sequencing data for 152 recombinant inbred (RI) strains from the BXD family of mice to map loci that modulate genome-wide patterns of new mutations arising during parent-to-offspring transmission at STRs. We defined quantitative phenotypes describing the numbers and types of germline STR mutations in each strain and performed quantitative trait locus (QTL) analyses for each of these phenotypes. We identified a locus on Chromosome 13 at which strains inheriting the C57BL/6J (B) haplotype have a higher rate of STR expansions than those inheriting the DBA/2J (D) haplotype. The strongest candidate gene in this locus isMsh3, a known modifier of STR stability in cancer and at pathogenic repeat expansions in mice and humans, as well as a current drug target against Huntington's disease. TheDhaplotype at this locus harbors a cluster of variants near the 5′ end ofMsh3, including multiple missense variants near the DNA mismatch recognition domain. In contrast, theBhaplotype contains a unique retrotransposon insertion. The rate of expansion covaries positively withMsh3expression—with higher expression from theBhaplotype. Finally, detailed analysis of mutation patterns showed that strains carrying theBallele have higher expansion rates, but slightly lower overall total mutation rates, compared with those with theDallele, particularly at tetranucleotide repeats. Our results suggest an important role for inherited variants inMsh3in modulating genome-wide patterns of germline mutations at STRs.