Large eukaryotes support diverse communities of microbes on their surface-epibiota-that profoundly influence their biology. Alternate factors known to structure complex patterns of microbial diversity-host evolutionary history and ecology, environmental conditions and stochasticity-do not act independently and it is challenging to disentangle their relative effects. Here, we surveyed the epibiota from 38 sympatric seaweed species that span diverse clades and have convergent morphology, which strongly influences seaweed ecology. Host identity explains most of the variation in epibiont communities and deeper host phylogenetic relationships (e.g., genus level) explain a small but significant portion of epibiont community variation. Strikingly, epibiota community composition is significantly influenced by host morphology and epibiota richness increases with morphological complexity of the seaweed host. This effect is robust after controlling for phylogenetic non-independence and is strongest for crustose seaweeds. We experimentally validated the effect of host morphology by quantifying bacterial community assembly on latex sheets cut to resemble three seaweed morphologies. The patterns match those observed in our field survey. Thus, biodiversity increases with habitat complexity in host-associated microbial communities, mirroring patterns observed in animal communities. We suggest that host morphology and structural complexity are underexplored mechanisms structuring microbial communities.