An emerging hallmark of many human diseases is transcription of typically silenced repetitive DNA containing pathogen-associated molecular patterns (PAMPs). These PAMPs engage the innate immune system via pattern recognition receptors (PRRs)-a phenomenon known as viral mimicry. We propose a statistical physics framework to quantify viral mimicry by measuring "selective forces" that enrich PAMPs compared to a genome-wide reference distribution. We validate our predictions by identifying repeats that bind different PRRs and show potential viral mimics in different repeat families across eukaryotic genomes, suggesting shared mechanisms drive emergence and retention. We propose two non-exclusive evolutionary hypotheses. The first "repeat-centric" hypothesis posits PAMPs are integral to the repeat life cycle and are therefore enriched as they mediate repeat expansion. The second "organism-centric" hypothesis proposes viral mimicry functions as a cell-intrinsic feedback mechanism for sensing and reacting to transcriptional dysregulation, which provides a selective pressure to maintain PAMPs in genomes.