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We show that a space-based gravitational microlensing survey for terrestrial extra-solar planets is feasible in the near future, and could provide a nearly complete picture of the properties of planetary systems in our Galaxy. We present simulations of such a survey using a 1-2m aperture space telescope with a ~2 square degree field-of-view which is used to continuously monitor ~10^8 Galactic bulge main sequence stars. The microlensing techniques allows the discovery of low mass planets with high signal-to-noise, and the space mission that we have studied are sensitive to planets with masses as low as that of Mars. By targeting main sequence source stars, which can only be resolved from space, the space-based microlensing survey is able to detect enough light from the lens stars to determine the spectral type of one third of the lens stars with detected planets, including virtually all of the F, G, and K stars which comprise one quarter of the event sample. This enables the determination of the planetary masses and separations in physical units, as well as the abundance of planets as a function of stellar type and distance from the Galactic center. We show that a space-based microlensing planet search program has its highest sensitivity to planets at orbital separations of 0.7-10 AU, but it will also have significant sensitivity at larger separations and will be able to detect free-floating planets in significant numbers. This complements the planned terrestrial planet transit missions which are sensitive to terrestrial planets at separations of =< 1 AU. Such a mission also detect ~50,000 giant planets via transits, and it is, therefore, the only proposed planet detection method that is sensitive to planets at all orbital radii.