This paper is devoted to the study of radiation of a massive spin-2 boson (graviton with a nonzero mass) through the event horizon of a generic static and spherically symmetric black hole in (3+1) dimensions. To this end, we consider the problem in the framework of the quantum tunneling phenomenon. We evaluate the tunneling rate of the massive gravitons by applying the semiclassical WKB approximation to the Fierz-Pauli equation. The temperature of the radiation is obtained with the aid of the Boltzmann expression. Our findings are in good agreement with the existing Hawking radiation studies in the current literature.