It is well known that moving magnetic textures may pump spin and charge currents along the direction of motion, a phenomenon called electronic pumping. Here, the electronic pumping arising from the steady motion of ferromagnetic skyrmions is investigated by solving the time evolution of the Schrödinger equation implemented on a tight-binding model with the statistical physics of the many-body problem. In contrast with rigid one-dimensional magnetic textures, we show that steadily moving magnetic skyrmions are able to pump large dc currents. This ability arises from their nontrivial magnetic topology, i.e., the coexistence of the spin-motive force and the topological Hall effect. Based on an adiabatic scattering theory, we compute the pumped current and demonstrate that it scales with the reflection coefficient of the conduction electrons against the skyrmion. In other words, in the semiclassical limit, reducing the size of the skyrmion and the width of the nanowire enhances this effect, making it scalable. We propose that such a phenomenon can be exploited in the context of racetrack devices, where the electronic pumping enhances the collective motion of the train of skyrmions.