To identify the characteristics of a suitable gas propellant for a microwave rocket, the discharge physics induced by an intense microwave in nitrogen, hydrogen, and helium was numerically reproduced by coupling a plasma fluid model with an electromagnetic wave propagation model. A discrete plasma structure was induced in nitrogen and hydrogen, because the ionization region was smaller than the incident-beam quarter wavelength. However, a diffusive plasma pattern was generated in helium, because the electron temperature increased and the electron-impact ionization was maintained even in the low-electric-field region. The shock wave propagation inside the rocket nozzle was numerically reproduced to evaluate the thrust performance dependence on the propellant species; this was achieved by solving the two-dimensional axisymmetric Euler equation with an energy source term for the microwave heating. The simple shock-tube theory indicated that the momentum coupling coefficient is proportional to the energy stored inside the rocket nozzle and inversely proportional to the propellant sound speed. The smallest momentum coupling coefficient was obtained for the helium case, although the sound speed in helium is faster than that in hydrogen. This was because insufficient energy was stored inside the rocket nozzle when helium was used, owing to the faster plasma propagation and lower energy absorption rate. The findings of this work indicate that to obtain a large thrust for a microwave rocket, selection of a gas propellant with a high energy absorption rate, small electron diffusion coefficient, low sound speed, and low specific heat ratio are preferable.