The problem of output feedback stabilizability of multi-input-multi-output (MIMO) multidimensional (n-D) linear systems is investigated using n-D polynomial matrix theory. A simple necessary and sufficient condition for output feedback stabilizability of a given MIMO n-D linear system is derived in terms of the generating polynomials associated with any matrix fraction descriptions of the system. When a given unstable plant is feedback stabilizable, constructive method is provided for obtaining a stabilizing compensator. Moreover, a strictly causal compensator can always be constructed for a causal (not necessarily strictly causal) plant. A non-trivial example is illustrated.