The paper proposes and analyzes a magnon-skrymion hybrid quantum system, consisting of a micromagnet and nearby magnetic skyrmions. The authors predict a strong coupling mechanism between the magnonic mode of the micromagnet and the quantized helicity degree of freedom of the skrymion. This setup allows for the induction of magnon-mediated nonreciprocal interactions and responses between distant skrymion qubits or between skrymion qubits and other quantum systems like superconducting qubits. The magnon mode in the YIG micromagnet, with its high spin density and low damping rate, is used to couple to the skrymion qubit, which behaves similarly to a superconducting charge qubit. The coherent coupling between the magnonic excitation and the skrymion qubit is described by the Jaynes-Cummings model, and the anisotropy of the YIG micromagnet results in the magnon-Kerr effect, allowing for exponential enhancement of the coupling strength. The paper also discusses the experimental feasibility of the proposed system, including the observation of Bloch skyrmions in frustrated magnets and the calculation of coupling strengths in multilayer structured hybrid systems. The work provides a quantum platform for investigating diverse quantum effects and quantum information processing with magnetic microstructures.The paper proposes and analyzes a magnon-skrymion hybrid quantum system, consisting of a micromagnet and nearby magnetic skyrmions. The authors predict a strong coupling mechanism between the magnonic mode of the micromagnet and the quantized helicity degree of freedom of the skrymion. This setup allows for the induction of magnon-mediated nonreciprocal interactions and responses between distant skrymion qubits or between skrymion qubits and other quantum systems like superconducting qubits. The magnon mode in the YIG micromagnet, with its high spin density and low damping rate, is used to couple to the skrymion qubit, which behaves similarly to a superconducting charge qubit. The coherent coupling between the magnonic excitation and the skrymion qubit is described by the Jaynes-Cummings model, and the anisotropy of the YIG micromagnet results in the magnon-Kerr effect, allowing for exponential enhancement of the coupling strength. The paper also discusses the experimental feasibility of the proposed system, including the observation of Bloch skyrmions in frustrated magnets and the calculation of coupling strengths in multilayer structured hybrid systems. The work provides a quantum platform for investigating diverse quantum effects and quantum information processing with magnetic microstructures.