The neutrino radiation from a completely relativistic electron gas in the presence of a large magnetic field (the neutrino analog of electromagnetic synchrotron radiation) is computed approximately, under the assumption of a direct electron-neutrino interaction. The radiation is also estimated in the case of a non-relativistic electron gas. It is shown that the radiation increases strongly with electron energy and magnetic-field strength, and is therefore most likely to have astrophysical significance in the evolution of stars with large electron energies and potentially large magnetic fields, such as white dwarfs. However, computation of the total neutrino luminosity of several model white dwarfs shows that the neutrino luminosity is limited by electron degeneracy to values much less than the photon luminosity. The process is also found to be relatively unimportant in the evolution of neutron stars.