Amplicons-large, highly identical segmental duplications-are a prominent feature of mammalian Y chromosomes. Although they encode genes essential for fertility, these amplicons differ vastly between species, and little is known about the selective constraints acting on them. Here, we develop computational tools to detect amplicon copy number with unprecedented accuracy from high-throughput sequencing data. We find that one-sixth (16.9%) of 1,216 males from the 1000 Genomes Project have at least one deleted or duplicated amplicon. However, each amplicon's reference copy number is scrupulously maintained among divergent branches of the Y chromosome phylogeny, including the ancient branch A00, indicating that the reference copy number is ancestral to all modern human Y chromosomes. Using phylogenetic analyses and simulations, we demonstrate that this pattern of variation is incompatible with neutral evolution and instead displays hallmarks of mutation-selection balance. We also observe cases of amplicon rescue, in which deleted amplicons are restored through subsequent duplications. These results indicate that, contrary to the lack of constraint suggested by the differences between species, natural selection has suppressed amplicon copy number variation in diverse human lineages.