A broadly accepted and stable biological classification system is a prerequisite for biological sciences. It provides the means to describe and communicate about life without ambiguity. Current biological classification and nomenclature use the species as the basic unit and require lengthy and laborious species descriptions before newly discovered organisms can be assigned to a species and be named. The current system is thus inadequate to classify and name the immense genetic diversity within species that is now being revealed by genome sequencing on a daily basis. To address this lack of a general intra-species classification and naming system adequate for today's speed of discovery of new diversity, we propose a classification and naming system that is exclusively based on genome similarity and that is suitable for automatic assignment of codes to any genome-sequenced organism without requiring any phenotypic or phylogenetic analysis. We provide examples demonstrating that genome similarity-based codes largely align with current taxonomic groups at many different levels in bacteria, animals, humans, plants, and viruses. Importantly, the proposed approach is only slightly affected by the order of code assignment and can thus provide codes that reflect similarity between organisms and that do not need to be revised upon discovery of new diversity. We envision genome similarity-based codes to complement current biological nomenclature and to provide a universal means to communicate unambiguously about any genome-sequenced organism in fields as diverse as biodiversity research, infectious disease control, human and microbial forensics, animal breed and plant cultivar certification, and human ancestry research.