Recently there has been a lot of interest in models in which gravity becomes strong at the TeV scale. The observed weakness of gravitational interactions is then explained by the existence of extra compact dimensions of space, which are accessible to gravity but not to standard model particles. We consider graviton emission into these extra dimensions from a hot supernova core. The phenomenology of SN 1987A places strong constraints on this energy loss mechanism, allowing us to derive a bound on the fundamental Planck scale. For the case of two extra dimensions we obtain a very strong bound of M greater than or similar to 50 TeV, which corresponds to a radius R less than or similar to 0.3 mu m.