Biological membranes have distinct geometries that confer specific functions. However, the molecular mechanisms underlying the phenomenological geometry/function correlations remain elusive. We studied the effect of membrane geometry on the localization of membrane-bound proteins. Quantitative comparative experiments between the two most abundant cellular membrane geometries, spherical and cylindrical, revealed that geometry regulates the spatial segregation of proteins. The measured geometry-driven segregation reached 50-fold for membranes of the same mean curvature, demonstrating a crucial and hitherto unaccounted contribution by Gaussian curvature. Molecular-field theory calculations elucidated the underlying physical and molecular mechanisms. Our results reveal that distinct membrane geometries have specific physicochemical properties and thus establish a ubiquitous mechanistic foundation for unravelling the conserved correlations between biological function and membrane polymorphism.