Magnetic skyrmion, a topologically stable spin-swirling object, can host emergent electromagnetism, as exemplified by the topological Hall effect and electric-current-driven skyrmion motion. To achieve efficient manipulation of nano-sized functional spin textures, it is imperative to exploit the resonant motion of skyrmions, analogously to the role of the ferromagnetic resonance in spintronics. The magnetic resonance of skyrmions has recently been detected with oscillating magnetic fields at 1-2 GHz, launching a search for new skyrmion functionality operating at microwave frequencies. Here we show a microwave magnetoelectric effect in resonant skyrmion dynamics. Through microwave transmittance spectroscopy on the skyrmion-hosting multiferroic crystal Cu₂OSeO₃ combined with theoretical simulations, we reveal nonreciprocal directional dichroism (NDD) at the resonant mode, that is, oppositely propagating microwaves exhibit different absorption. The microscopic mechanism of the present NDD is not associated with the conventional Faraday effect but with the skyrmion magnetoelectric resonance instead, suggesting a conceptually new microwave functionality.