Copy number variants (CNVs) represent a substantial source of genomic variation in vertebrates and have been associated with numerous human diseases. Despite this, the extent of CNVs in the zebrafish, an important model for human disease, remains unknown. Using 80 zebrafish genomes, representing three commonly used laboratory strains and one native population, we constructed a genome-wide, high-resolution CNV map for the zebrafish comprising 6,080 CNV elements and encompassing 14.6% of the zebrafish reference genome. This amount of copy number variation is four times that previously observed in other vertebrates, including humans. Moreover, 69% of the CNV elements exhibited strain specificity, with the highest number observed for Tubingen. This variation likely arose, in part, from Tubingen's large founding size and composite population origin. Additional population genetic studies also provided important insight into the origins and substructure of these commonly used laboratory strains. This extensive variation among and within zebrafish strains may have functional effects that impact phenotype and, if not properly addressed, such extensive levels of germ-line variation and population substructure in this commonly used model organism can potentially confound studies intended for translation to human diseases.