Ferromagnetism and superconductivity are most fundamental phenomena in condensed-matter physics. Entailing opposite spin orders, they share an important conceptual similarity: disturbances in magnetic ordering in magnetic materials can propagate in the form of spin waves (magnons) while magnetic fields penetrate superconductors as a lattice of magnetic flux quanta (fluxons). Despite a rich choice of wave and quantum phenomena predicted, magnon–fluxon coupling has not been observed experimentally so far. Here, we clearly evidence the interaction of spin waves with a flux lattice in ferromagnet/superconductor Py/Nb bilayers. We demonstrate that, in this system, the magnon frequency spectrum exhibits a Bloch-like band structure that can be tuned by the biasing magnetic field. Furthermore, we observe Doppler shifts in the frequency spectra of spin waves scattered on a flux lattice moving under the action of a transport current in the superconductor.