Spin wave logic circuits using quantum oscillations of spins (magnons) as carriers of information have been proposed for next generation computing with reduced energy demands and the benefit of easy parallelization. Current realizations of magnonic devices have micrometer sized patterns. Here we demonstrate the feasibility of biogenic nanoparticle chains as the first step to truly nanoscale magnonics at room temperature. Our measurements on magnetosome chains (ca 12 magnetite crystals with 35 nm particle size each), combined with micromagnetic simulations, show that the topology of the magnon bands, namely anisotropy, band deformation, and band gaps are determined by local arrangement and orientation of particles, which in turn depends on the genotype of the bacteria. Our biomagnonic approach offers the exciting prospect of genetically engineering magnonic quantum states in nanoconfined geometries. By connecting mutants of magnetotactic bacteria with different arrangements of magnetite crystals, novel architectures for magnonic computing may be (self-) assembled.