Well-powered genome-wide association studies, now made possible through advances in technology and large-scale collaborative projects, promise to characterize the contribution of rare variants to complex traits and disease. However, while population structure is a known confounder of association studies, it remains unknown whether methods developed to control stratification are equally effective for rare variants. Here, we demonstrate that rare variants can show a stratification that is systematically different from, and typically stronger than, common variants, and this is not necessarily corrected by existing methods. We show that the same process leads to inflation for load-based tests and can obscure signals at truly associated variants. Furthermore, we show that populations can display spatial structure in rare variants, even when Wright's fixation index F(ST) is low, but that allele frequency-dependent metrics of allele sharing can reveal localized stratification. These results underscore the importance of collecting and integrating spatial information in the genetic analysis of complex traits.