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Optically active spin defects in wide bandgap semiconductors serve as a local sensor of multiple degrees of freedom in a variety of “hard” and “soft” condensed matter systems. Taking advantage of the recent progress on quantum sensing using van der Waals (vdW) quantum materials, here we report direct measurements of spin waves excited in magnetic insulator Y₃Fe₅O₁₂(YIG) by boron vacancy $V_{\mathrm{B}}^{-}$spin defects contained in few-layer-thick hexagonal boron nitride nanoflakes. We show that the ferromagnetic resonance and parametric spin excitations can be effectively detected by $V_{\mathrm{B}}^{-}$spin defects under various experimental conditions through optically detected magnetic resonance measurements. The off-resonant dipole interaction between YIG magnons and $V_{\mathrm{B}}^{-}$spin defects is mediated by multi-magnon scattering processes, which may find relevant applications in a range of emerging quantum sensing, computing, and metrology technologies. Our results also highlight the opportunities offered by quantum spin defects in layered two-dimensional vdW materials for investigating local spin dynamic behaviors in magnetic solid-state matters.