We investigate theoretically the optical properties of a hybrid optomechanical system embedded with a yttrium iron garnet (YIG) sphere. It is considered that YIG interacts with a single mode of the microcavity through magnetic dipole coupling. To enhance the magnomechanical coupling, the magnon mode is directly driven by a microwave field. The microcavity is driven by the control and probe field. The study of steady-state dynamics of the system shows bistable behavior. Furthermore, optomechanically induced transparency under the influence of a strong control field in the system is explored. In addition, magnomechanically induced transparency (MMIT) due to the presence of nonlinear magnon–phonon interaction is studied. Fano like shape is observed in MMIT. The impact of different system parameters is studied. Our results will provide a theoretical approach to understand opto-magnomechanical systems. These results may be useful in all optical switching devices and optical transistors.