Genomes usually contain some non-repetitive sequences that are missing from the reference genome and occur only in a population subset. Such non-repetitive, non-reference (NRNR) sequences have remained largely unexplored in terms of their characterization and downstream analyses. Here we describe 3,791 breakpoint-resolved NRNR sequence variants called using PopIns from whole-genome sequence data of 15,219 Icelanders. We found that over 95% of the 244 NRNR sequences that are 200 bp or longer are present in chimpanzees, indicating that they are ancestral. Furthermore, 149 variant loci are in linkage disequilibrium (r2 > 0.8) with a genome-wide association study (GWAS) catalog marker, suggesting disease relevance. Additionally, we report an association (P = 3.8 × 10-8, odds ratio (OR) = 0.92) with myocardial infarction (23,360 cases, 300,771 controls) for a 766-bp NRNR sequence variant. Our results underline the importance of including variation of all complexity levels when searching for variants that associate with disease.