Structured transfer matrix systems are linear systems given by transfer matrices of which the infinite zero order of each nonzero entry is known, while the associated infinite gains are unknown and assumed mutually independent. In this paper necessary and sufficient conditions are derived for the generic solvability of the well-known disturbance decoupling problem by measurement feedback for structured transfer matrix systems. Generic solvability here means solvability for almost all possible values for the infinite gains of the nonzero transfer matrix entries. The conditions will be stated in terms of a bipartite graph that can be easily associated with a structured transfer matrix system. The advantage of this is that the conditions then can be verified by means of graph theoretic algorithms.