Arbuscular mycorrhizal fungi (phylum Glomeromycota) are among the oldest and most successful symbionts of land plants. With no evidence of sexual reproduction, their evolutionary success is inconsistent with the prediction that asexual taxa are vulnerable to extinction due to accumulation of deleterious mutations. To explore why Glomeromycota defy this prediction, we studied ribosomal RNA (rRNA) gene evolution in the Claroideoglomus lineage and estimated effective population size, Ne, in C. etunicatum. We found that rRNA genes of these fungi exhibit unusual and complex patterns of molecular evolution. In C. etunicatum, these patterns can be collectively explained by an unexpectedly large Ne combined with imperfect genome-wide and population-level rRNA gene repeat homogenization. The mutations accumulated in rRNA gene sequences indicate that natural selection is effective at purging deleterious mutations in the Claroideoglomus lineage, which is also consistent with the large Ne of C. etunicatum. We propose that in the near absence of recombination, asexual reproduction involving massively multinucleate spores typical for Glomeromycota is responsible for the improved efficacy of selection relative to drift. We postulate that large effective population sizes contribute to the evolutionary longevity of Glomeromycota.