The ability of atomic hydrogen to chemisorb on graphene makes the latter a promising material for hydrogen storage. Based on scanning tunneling microscopy techniques, we report on site-selective adsorption of atomic hydrogen on convexly curved regions of monolayer graphene grown on SiC(0001). This system exhibits an intrinsic curvature owing to the interaction with the substrate. We show that at low coverage hydrogen is found on convex areas of the graphene lattice. No hydrogen is detected on concave regions. These findings are in agreement with theoretical models which suggest that both binding energy and adsorption barrier can be tuned by controlling the local curvature of the graphene lattice. This curvature-dependence combined with the known graphene flexibility may be exploited for storage and controlled release of hydrogen at room temperature making it a valuable candidate for the implementation of hydrogen-storage devices.