Bessel-Gauss beams (BGBs) have been widely investigated in optics in the paraxial approximation, under the frame of a scalar wave theory. Such approximations no longer hold in the microwave/millimeter-wave range, where the vectorial nature of electromagnetic fields cannot be neglected, and experimental realizations of BGBs are still lacking. In this work, we discuss the generation of BGBs through a fully vectorial electromagnetic approach. The field derivation and the numerical evaluation of a BGB are first illustrated. A possible scheme for realizing such solutions is outlined, thus paving the way for the first experimental realization of BGBs at microwave frequencies.