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MWC 349A is a massive star with a well-known circumstellar disk rotating following a Keplerian law, and an ionized wind launched from the disk surface. Recent ALMA observations carried out toward this system have however revealed an additional high-velocity component in the strong, maser emission of hydrogen radio recombination lines (RRLs), suggesting the presence of a high-velocity ionized jet. In this work, we present 3D non-LTE radiative transfer modeling of the emission of the H30$\alpha$ and H26$\alpha$ maser lines, and of their associated radio continuum emission, toward the MWC 349A massive star. By using the MORELI code, we reproduce the spatial distribution and kinematics of the high-velocity emission of the H30$\alpha$ and H26$\alpha$ maser lines with a high-velocity ionized jet expanding at a velocity of $\sim$ 250 km s$^{-1}$, surrounded by MWC 349A's wide-angle ionized wind. The bipolar jet, which is launched from MWC 349A's disk, is poorly collimated and slightly miss-aligned with respect to the disk rotation axis. Thanks to the unprecedented sensitivity and spatial accuracy provided by ALMA, we also find that the already known, wide-angle ionized wind decelerates as it expands radially from the ionized disk. We briefly discuss the implications of our findings in understanding the formation and evolution of massive stars. Our results show the huge potential of RRL masers as powerful probes of the innermost ionized regions around massive stars and of their high-velocity jets.