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In many theoretical frameworks our visible world is a 3-brane, embedded in a multidimensional bulk, possibly coexisting with hidden braneworlds. Some works have also shown that matter swapping between braneworlds can occur. Here we report the results of an experiment – at the Institut Laue-Langevin (Grenoble, France) – designed to detect thermal neutron swapping to and from another braneworld, thus constraining the probability p2 of such an event. The limit, p<4.6×10−10 at 95% C.L., is 4 orders of magnitude better than the previous bound based on the disappearance of stored ultracold neutrons. In the simplest braneworld scenario, for two parallel Planck-scale branes separated by a distance d, we conclude that d>87 in Planck length units.