The hotspots of structural polymorphisms and structural mutability in the human genome remain to be explained mechanistically. We examine associations of structural mutability with germline DNA methylation and with non-allelic homologous recombination (NAHR) mediated by low-copy repeats (LCRs). Combined evidence from four human sperm methylome maps, human genome evolution, structural polymorphisms in the human population, and previous genomic and disease studies consistently points to a strong association of germline hypomethylation and genomic instability. Specifically, methylation deserts, the ~1% fraction of the human genome with the lowest methylation in the germline, show a tenfold enrichment for structural rearrangements that occurred in the human genome since the branching of chimpanzee and are highly enriched for fast-evolving loci that regulate tissue-specific gene expression. Analysis of copy number variants (CNVs) from 400 human samples identified using a custom-designed array comparative genomic hybridization (aCGH) chip, combined with publicly available structural variation data, indicates that association of structural mutability with germline hypomethylation is comparable in magnitude to the association of structural mutability with LCR-mediated NAHR. Moreover, rare CNVs occurring in the genomes of individuals diagnosed with schizophrenia, bipolar disorder, and developmental delay and de novo CNVs occurring in those diagnosed with autism are significantly more concentrated within hypomethylated regions. These findings suggest a new connection between the epigenome, selective mutability, evolution, and human disease.