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Hybrid quantum systems consisting of nitrogen-vacancy (NV) centers in diamond and magnons in ferrimagnets have recently attracted much attention as a platform for on-chip long-distance entanglement, interfacing quantum information science with magnonics. Here, we experimentally determine the magnon-induced self-interaction of this hybrid system by combining longitudinal (T 1) relaxometry measurements with the fluctuation-dissipation and Kramers-Kronig relations. This self-interaction is a function of the NV-magnon coupling strength and thereby provides an estimate of the magnon-mediated two-qubit interaction. Our results, including the enhanced T 1 relaxation rates caused by magnetostatic surface magnons are quantitatively consistent with a model in which the NV center is coupled to magnons by the magnetic dipole interactions. These findings help build a foundation for the hybrid quantum …