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 is Msh3, 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. The D haplotype at this locus harbors a cluster of variants near the 5' end of Msh3, including multiple missense variants near the DNA mismatch recognition domain. In contrast, the B haplotype contains a unique retrotransposon insertion. The rate of expansion covaries positively with Msh3 expression-with higher expression from the B haplotype. Finally, detailed analysis of mutation patterns showed that strains carrying the B allele have higher expansion rates, but slightly lower overall total mutation rates, compared with those with the D allele, particularly at tetranucleotide repeats. Our results suggest an important role for inherited variants in Msh3 in modulating genome-wide patterns of germline mutations at STRs.