We present a theoretical approach to use ferro- or ferrimagnetic nanoparticles as microwave nanomagnonic cavities to concentrate microwave magnetic fields into deeply subwavelength volumes ∼10⁻¹³ mm³. We show that the field in such nanocavities can efficiently couple to isolated spin emitters (spin qubits) positioned close to the nanoparticle surface reaching the single magnon-spin strong-coupling regime and mediate efficient long-range quantum state transfer between isolated spin emitters. Nanomagnonic cavities thus pave the way towards magnon-based quantum networks and magnon-mediated quantum gates.