Different extensions of the standard model of particle physics, such as braneworld or mirror matter models, predict the existence of a neutron sterile state, possibly as a dark matter candidate. This Letter reports a new experimental constraint on the probability p for neutron conversion into a hidden neutron, set by the STEREO experiment at the high flux reactor of the Institut Laue-Langevin. The limit is p<3.1×10^{-11} at 95% C.L. improving the previous limit by a factor of 13. This result demonstrates that short-baseline neutrino experiments can be used as competitive passing-through-walls neutron experiments to search for hidden neutrons.