This contribution is concerned with deriving the canonical scattering of a time-harmonic electromagnetic Gaussian propagator from a fast moving perfectly conducting circular cylinder under the framework of Einstein's Special Relativity. The incident electromagnetic wave objects in this contribution serve as the basis wave propagators of the frame-based phase-space beam summation method, which is a general framework for analyzing radiation from extended sources. The incident Gaussian beam propagator is readily given by its plane wave spectral representation in the laboratory frame. By utilizing the Lorentz transformation and applying Maxwell's boundary conditions in the co-moving frame, we obtain an exact solution for the scattered fields vector potentials in the form of spectral integrals. The later are evaluated asymptotically for high frequencies (of the incident field) and transformed back to the laboratory frame via the inverse Lorentz transformation.