All multicellular organisms are genetic mosaics owing to somatic mutations. The accumulation of somatic genetic variation in clonal species undergoing asexual (or clonal) reproduction may lead to phenotypic heterogeneity among autonomous modules (termed ramets). However, the abundance and dynamics of somatic genetic variation under clonal reproduction remain poorly understood. Here we show that branching events in a seagrass (Zostera marina) clone or genet lead to population bottlenecks of tissue that result in the evolution of genetically differentiated ramets in a process of somatic genetic drift. By studying inter-ramet somatic genetic variation, we uncovered thousands of single nucleotide polymorphisms that segregated among ramets. Ultra-deep resequencing of single ramets revealed that the strength of purifying selection on mosaic genetic variation was greater within than among ramets. Our study provides evidence for multiple levels of selection during the evolution of seagrass genets. Somatic genetic drift during clonal propagation leads to the emergence of genetically unique modules that constitute an elementary level of selection and individuality in long-lived clonal species.