The ability to switch the polarization of a transmitted electromagnetic wave from vertical to horizontal, or vice versa, is of great technological interest because of its many applications in long distance communication. Binary bits can be encoded in two orthogonal polarizations and transmitted securely from point to point. Polarization switches, however, are usually much larger than the wavelength of the electromagnetic wave. Consequently, most research in this area has focused on the optical regime where the wavelength is relatively short (~1 micron), so that the switch being much larger than the wavelength is not too inconvenient. However, this changes in the microwave regime where the wavelength is much larger (typically > 1 cm). That makes a microwave ultra-sub-wavelength polarization switch very attractive. Here, we report such a switch made of an array of magnetostrictive nanomagnets (~100 nm lateral dimension) deposited on a piezoelectric substrate to make an "artificial magnonic crystal". A surface acoustic wave (SAW) launched in the substrate with suitable electrodes excites spin waves in the nanomagnets via phonon-magnon coupling, resulting in radiation of electromagnetic waves via magnon-photon coupling. The polarization of the beam radiated in a given direction at a given frequency can be rotated through ~90 degrees by changing the direction of SAW propagation in the substrate to implement the polarization switch.