  Theories involving extra dimensions, a low (TeV) string scale and bulk
singlet neutrinos will produce an effective neutrino magnetic moment which may
be large (< 10^{-11} mu_B). The effective magnetic moment increases with
neutrino energy, and therefore high energy reactions are most useful for
limiting the allowed number of extra dimensions. We examine constraints from
both neutrino-electron scattering and also astrophysical environments. We find
that supernova energy loss considerations require a number of extra dimensions,
n > 1, for an electron neutrino-bulk neutrino Yukawa coupling of order 1.
