Hybridized magnonic-photonic systems promise novel applications for future information processing technologies. Here, a hybrid magnonic system comprising of a qutrit (𝚲-type three-level atom) and a ferromagnetic YIG sphere is considered. Indeed, the whole system is driven by two light fields under the influence of the thermal environment. The indirect magnon-atom interaction is established via the virtual photon exchange. The associated Lindblad master equation is derived and its solution is found to investigate the nonclassical feature, especially in the steady-state solution. Generally, the system shows considerable nonclassicality, that is, strong magnon antibunching and magnon blockade. In fact, the feasibility of using such a hybrid system to prepare a single-magnon source based on magnon blockade effects we theoretically demonstrated. Besides, the considered system may be exploited to generate robust and stable magnon-atom entanglement. The appearance of magnon blockade and magnon-atom entanglement in the 𝚲-type atom may have its origin in the fact that the atom is trapped in different superposition states, induced by the quantum interference phenomenon. The proposed model and the corresponding results may open up an intriguing prospect to prepare a single-magnon source and provide further benefits through concatenating with photons in optomagnonic systems.