Pathogens compete for hosts through patterns of cross-protection conferred by immune responses to antigens. In Plasmodium falciparum malaria, the var multigene family encoding for the major blood-stage antigen PfEMP1 has evolved enormous genetic diversity through ectopic recombination and mutation. With 50-60 var genes per genome, it is unclear whether immune selection can act as a dominant force in structuring var repertoires of local populations. The combinatorial complexity of the var system remains beyond the reach of existing strain theory and previous evidence for non-random structure cannot demonstrate immune selection without comparison with neutral models. We develop two neutral models that encompass malaria epidemiology but exclude competitive interactions between parasites. These models, combined with networks of genetic similarity, reveal non-neutral strain structure in both simulated systems and an extensively sampled population in Ghana. The unique population structure we identify underlies the large transmission reservoir characteristic of highly endemic regions in Africa.