In this work, a theoretical framework is developed for the multiple scattering of an anti-plane shear wave by a functionally graded multiferroic fibrous composite. The composite consists of arbitrarily distributed circular cylinders and may have different sizes and material constituents. The cylinders are exponentially graded along the radial direction. We exploit the multipole expansions, transition matrix, and Graf’s addition/binomial expansion theorems to obtain a complete solution of the multiple scattering problem in the scenario of functionally graded multiferroic composites. These solved magneto-electro-elastic fields are then used to obtain the directivity patterns of the scattered wave, dynamic stress (electric displacement/magnetic flux) concentration factors, and scattering cross sections. Numerical results reveal the profound influence of the functionally graded parameter, the material properties of constituent phases, the number of inclusions, as well as the frequency of a propagating SH wave on the scattered field induced by the functionally graded fibers. It is expected that the formulation and numerical results serve as useful references for the design and manufacture of functionally graded piezoelectric–piezomagnetic fibrous composites under dynamic loadings.