<p>Cherenkov radiation is a universal phenomenon that arises from a uniformly moving source. It enables wave emission and finds important applications across various fields of physics, from particle physics to plasmonics. Efforts to explore the Cherenkov emission of coherent spin waves, or magnons, are currently limited by the absence of experimentally realized fast-moving magnetic perturbations. Here we demonstrate the magnon-Cherenkov effect by showing the emission of exchange spin waves. This emission is enabled by an optically induced picosecond strain pulse that acts as a spatially localized propagating perturbation of the internal effective magnetic field as a result of magnetoelastic coupling. We observe the propagation of a strain pulse through the thickness of a dielectric ferrimagnet, followed by the emission of spin waves that fully satisfy the conditions for the Cherenkov effect. The spectral characteristics of the emitted spin waves are controlled with an applied magnetic field and the shape of the strain pulse. Therefore, our results expand the possibilities to realize and control non-dissipative spin transport in various laterally and vertically structured magnonic devices.</p>