Magnon and photon blockade implementation and manipulation have significant practical applications in quantum information processing and quantum metrology due to their tight relations to single-photon and -magnon source devices. In this paper, we propose an experimentally feasible hybrid scheme for the dynamical description of the tripartite interacting system consisting of magnon and phonon modes with photons in an optomechanical system, from which we aim to explore the quantum statistics, as well as the magnon and photon blockade phenomenon. To achieve the purpose, the dissipative solution of the system is obtained with the help of the Lindblad master equation. Via employing the equal-time second-order correlation function and using the steady state solution of the system, the statistics and blockade effects of magnon and photon are analyzed and also their dependence on the parameters involved in the system are discussed. Utilizing feasible parameters, our simulations illustrate that, sub-Poissonian behavior and therefore, blockade of magnon and photon are simultaneously achieved. More importantly, the mentioned blockade effects can be obtained in a range of parameters (and not with specific) which makes our proposal easy to access, experimentally. Considering the above realizations, the introduced scheme opens up a pathway to design single-magnon and - photon generators, which are of crucial importance in advanced quantum science and technologies.