Wrinkling of spherical surfaces represents a promising pathway for the formation of complex hierarchical structures and patterns. Using a swelling-based approach, we demonstrate the relationship between applied compressive stress, radius of curvature, and wrinkle pattern morphology. Surface features with spherical curvature are fabricated on poly(dimethylsiloxane) elastomers and a stiff surface oxide layer is generated using UV–ozone treatment. Swelling of this surface layer with ethanol vapor results in the formation of periodic wrinkles on the spherical caps. The radius of curvature is found to influence the critical wrinkling stress of the system, allowing cap size to independently dictate wrinkle morphology from non-wrinkled caps at small radii, through hexagonal dimple and long ridge structures as the cap radius increases. A similar transition is observed at constant radius by varying the UV–ozone treatment time, which affects the oxide film thickness and composition. The influence of curvature on the critical wrinkling stress is confirmed by modulating the atmospheric concentration of ethanol, and measuring the applied stress for the lowest concentration for which wrinkling occurs.