Time-dependent, radiative instabilities in the creation and transport of polarized astrophysical maser radiation in the presence of a magnetic field are calculated. The instabilities are similar to and occur under the same conditions as those found previously by Scappaticci & Watson for unpolarized maser radiation. The common limits in which the Zeeman splitting is much greater than, and much less than, the spectral line breadths are both considered in the current investigation. The resulting fluctuations in the emergent radiation are potentially relevant for the OH 1665 MHz masers which have been reported to fluctuate on timescales of 1000 s and which tend to be polarized. Instabilities occur and alter the transport of maser radiation only under a quite limited range of conditions. In particular, we find here that the instabilities do not occur for conditions that are appropriate for astrophysical masers with small Zeeman splittings such as the SiO and H2O masers. The time-independent, numerical solutions to the GKK equations of radiative transfer that have been obtained in previous investigations are thus essentially always valid except within a narrow range of conditions relevant for the OH masers.