For sufficiently rapid zero-order hold (ZOH) sampling, it is known that the zeros of single-input, single-output discrete-time systems expressed in the forward shift operator converge to values determined only by the degrees of the finite and infinite zeros of the underlying continuous-time system. In this paper, we show how this result can be generalized to multi-input, multi-output (MIMO) systems decouplable by static state feedback (equivalently, having a diagonal interactor matrix). In the fast sampling limit, we show how invariant and infinite zero structure is mapped under ZOH sampling for discrete-time systems expressed in either the delta (forward difference) or shift operators.