Observations of double-peaked, masing H29-alpha, H30-alpha, and H31-alpha radio recombination lines (RRLs), at 256-210 GHz, from the binary star system MWC 349 show variations over a period of 2 yr. Both the velocity separation of the peaks and the intensity ratio V/R of the violet (V)- and red (R)-shifted components vary similarly to what has been observed in optical and IR lines from Be stars. The average velocity of the V and R components remains constant at 8.2 km s-1, marking the radial velocity of MWC 349A and suggesting a kinematic origin for the RRLs. Using the model proposed for MWC 349A by Hamann & Simon from optical and IR emission lines, this paper suggests that the time-varying RRLs come from the outer region (radius almost-equal-to 22-30 AU) of a circumstellar disk in Keplerian rotation embedded in the much larger, expanding, ionized region (radius almost-equal-to 200 AU) that encloses the entire star and disk system. The variable velocities then result from changes in radial position within the Keplerian disk. As wavelength increases from 1 mm, the masing RRLs from the inner disk weaken, and the free-free opacity of the outer region increases. The composite RRL line profiles seen by an observer become increasingly dominated by contributions from the expanding region enclosing the MWC 349A circumstellar disk, as evidenced by the progressive negative shift of the V(lsr)s observed for RRLs at 3 mm and 13 mm.