In the living cell, proteins are able to organize space much larger than their dimensions. In return, changes of intracellular space can influence biochemical reactions, allowing cells to sense their size and shape. Despite the possibility to reconstitute protein self-organization with only a few purified components, we still lack knowledge of how geometrical boundaries affect spatiotemporal protein patterns. Following a minimal systems approach, we used purified proteins and photolithographically patterned membranes to study the influence of spatial confinement on the self-organization of the Min system, a spatial regulator of bacterial cytokinesis, in vitro. We found that the emerging protein pattern responds even to the lateral, two-dimensional geometry of the membrane such that, as in the three-dimensional cell, Min protein waves travel along the longest axis of the membrane patch. This shows that for spatial sensing the Min system does not need to be enclosed in a three-dimensional compartment. Using a computational model we quantitatively analyzed our experimental findings and identified persistent binding of MinE to the membrane as requirement for the Min system to sense geometry. Our results give insight into the interplay between geometrical confinement and biochemical patterns emerging from a nonlinear reaction-diffusion system.